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A LITERATURE SURVEY ON QUEUEING MODEL WITH WORKING VACATION

Divya K., Indhira K.

In 2002, the Working Vacation (WV) queues were implemented as an extension of standard queueing models with vacations. During the vacation period in WV queues, the server provides service at a slower pace as opposed to the typical busy period.The objective of this survey is to provide a concise overview of the latest scholarly investigations on queueing models for WVs. The concept of a queue with WV has been implemented across various domains, encompassing computer systems, communication networks, production management, computer communication, manufacturing, and inventory systems. Additionally, it has been applied to network service, web service, file transfer service, and mail service.

Cite: Divya K., Indhira K. A LITERATURE SURVEY ON QUEUEING MODEL WITH WORKING VACATION. Reliability: Theory & Applications. 2024, March 1(77): 40-49, DOI: https://doi.org/10.24412/1932-2321-2024-177-40-49

BAYESIAN ESTIMATION OF TOPP-LEONE LINDLEY (TLL) DISTRIBUTION PARAMETERS UNDER DIFFERENT LOSS FUNCTIONS USING LINDLEY APPROXIMATION

Nzei C. Lawrence, Adegoke M. Taiwo, Ekhosuehi N., Mbegbu I. Julian

In this study, we present the Bayesian estimates of the unknown parameters of the Topp-Leone Lindley distribution using the maximum likelihood and Bayesian methods. In this study, the Bayes theorem was adopted for obtaining the posterior distribution of the shape parameter and scale parameter of the Topp-Leone Lindley distribution assuming the Jeffreys’ (non-informative) prior for the shape parameter and the Gamma (conjugate) prior for the scale parameter under three different loss functions namely: Square Error Loss Function, Linear Exponential Loss Function and Generalized Entropy Loss Function. The posterior distribution derived for both parameters are not solvable analytically, it requires a numerical approximation techniques to obtain the solution. The Lindley approximation techniques was adopted to obtain the parameters of interest. The loss function were used to derive the estimates of both parameters with an assumption that the both parameters are unknown and independent. To ascertain the accuracy of these estimators, the proposed Bayesian estimators under different loss functions are compared with the corresponding maximum likelihood estimator using a Monte Carlo simulation on the performance of these estimators according to the mean square error and BIAS based on simulated samples simulated from the Topp-Leone Lindley distribution. . It was also observed for any fixed value of the parameters, as sample size increases, the mean square errors of the Bayesian Estimates and maximum likelihood estimates decrease. Also, the maximum likelihood estimates and Bayesian estimates converge to the same value as the sample gets larger except for Generalized Entropy Loss Function.

Cite: Nzei C. Lawrence, Adegoke M. Taiwo, Ekhosuehi N., Mbegbu I. Julian  BAYESIAN ESTIMATION OF TOPP-LEONE LINDLEY (TLL) DISTRIBUTION PARAMETERS UNDER DIFFERENT LOSS FUNCTIONS USING LINDLEY APPROXIMATION. Reliability: Theory & Applications. 2024, March 1(77): 50-64, DOI: https://doi.org/10.24412/1932-2321-2024-177-50-64

SINE-WEIBULL DISTRIBUTION: MATHEMATICAL PROPERTIES AND APPLICATION TO REAL DATASETS

Muhammad Umar Faruk, Alhaji Modu Isa, Aishatu Kaigama

New parameters can be added to expand families of distribution for greater flexibility or to construct covariate models in several ways. In this study, a trigonometric-type distribution called Sine-Weibull distribution was developed by adopting the Weibull distribution as the baseline distribution and Sine-G Family as the generator to generate a flexible probability distribution without the need for extra parameters. The moment, moment generating function, entropy, and order statistics are some of the mathematical aspects of this distribution that were derived. The Maximum Likelihood approach was used to estimate the new distribution's parameters. Using actual datasets, the Sine-Weibull distribution's applicability was demonstrated.

Cite: Muhammad Umar Faruk, Alhaji Modu Isa, Aishatu Kaigama  SINE-WEIBULL DISTRIBUTION: MATHEMATICAL PROPERTIES AND APPLICATION TO REAL DATASETS. Reliability: Theory & Applications. 2024, March 1(77): 65-72, DOI: https://doi.org/10.24412/1932-2321-2024-177-65-72

RECENT DEVELOPMENTS IN THE COMPUTATION OF THE ROCOF OF MULTI-STATE SYSTEMS AND ITS APPLICATIONS

Guglielmo D’Amico, Fulvio Gismondi

This paper reviews several theoretical works on the computation of the Rate of Occurrence of Failure (ROCOF) for general multi-state random systems, focusing on recent generalizations. The discussion begins by defining the ROCOF for a Markov process and discussing the main results achieved in the literature, then moves towards the richer framework represented by semi-Markov systems. The paper discusses complications that arise when extending the ROCOF to higher orders so that a measure of the association of failures in time can be obtained. The work then analyzes possible modifications in terms of a conditional version of the ROCOF, which is of special interest in applications. The findings are illustrated by a numerical example from reliability, and the broad applicability is demonstrated by a discussion of different applications in other domains.

Cite: Guglielmo D’Amico, Fulvio Gismondi RECENT DEVELOPMENTS IN THE COMPUTATION OF THE ROCOF OF MULTI-STATE SYSTEMS AND ITS APPLICATIONS. Reliability: Theory & Applications. 2024, March 1(77): 73-85, DOI: https://doi.org/10.24412/1932-2321-2024-177-73-85

STRIP-PLOT ANALYSIS FOR THE CONSTRUCTION OF COMPLETE TRIPARTITE AND CUBIC GRAPHS             

V. Saranya, S. Kavitha

The Strip-Plot Design (SPD) is plays an important role in the complete block designs and also using the agricultural, medical and industry fields. SPD is best suited for a two-factor experiment that has more treatments than can be accommodated by a complete block design. In a SPD, one factor is assigned to the horizontal strip plot, one factor is assigned to the vertical – strip plot and one factor is interaction plot. Also, few experimental materials may be rare while other test items may be available in altering doses of other therapeutic factors, which may be expensive or time-consuming. One of the main features of SPD involves three types of experimental errors: row - strip plot error, coloum – strip plot error and interaction plot error. Experimenting across processing steps is essential for studying the interaction of factors where certain factors come from one step and others arrive from the other. The strip-plot design is a very efficient design for investigating multiple-step processes in terms of both resources and time. Strip-plot designs are economical when the factors are hard to change and the process under research has three discrete stages. When we want to study interactions between factors where some factors are from one step and other factors from another step, it is important to conduct experiments across processing steps. The approach is flexible because it can handle experimental design problems involving factors acting at different levels, unlike the existing method. Graphs are widely used representations of both natural and human-made structures. Graph theory can be used to investigate "things that are connected to other things. “Fits nearly everywhere. Some tough problems become easier to solve when they are represented graphically. We reviewed the agricultural field yield of the strip-plot design and early work on the design of industrial strip-plot design in this paper. We have also described the model of strip-plot design. We, therefore, advise experimenters to ensure that their strip-plot designs contain a sufficient number of rows and columns so that valid statistical inference is possible. A bipartite graph is one in which the edges can be divided into two sets without going into sets. A complete bipartite graph is a bipartite graph that is completed. The complete tripartite graph in which the edges can be divided into three set without going into sets. The cubic graph is a graph in which all vertices have degree three. This paper describes the construction and Statistical Analysis of SPD using some particular types of graphs is discussed through numerical examples.

Cite: V. Saranya, S. Kavitha  STRIP-PLOT ANALYSIS FOR THE CONSTRUCTION OF COMPLETE TRIPARTITE AND CUBIC GRAPHS . Reliability: Theory & Applications. 2024, March 1(77): 86-99, DOI: https://doi.org/10.24412/1932-2321-2024-177-86-99

A HYBRID APPROACH TO SINGLE ACCEPTANCE SAMPLING PLANS FOR LIFETIMES MODELED WITH THE EXPONENTIAL RAYLEIGH DISTRIBUTION

Nandhini M, Radhika A, Jeslin J, Manigandan P

This article explores into the examination of a novel compound distribution termed the "Exponential Rayleigh distribution" in the context of truncated life testing within a sampling plan. It introduces a hybrid single acceptance sampling plan tailored for truncated life testing scenarios where the item's lifespan adheres to the Exponential Rayleigh distribution. One of the primary segments within the domain of product quality control is referred to as “sampling inspection by variables”. This category encompasses procedures that involve the selection of multiple individual units based on measurements taken from a sample to assess a specific quality attribute under scrutiny. These plans, used to assess whether to accept or reject a submitted batch of items based on their observed lifetimes, are commonly known as reliability test plans. The article also outlines the development of a test plan to determine when to conclude the experiment given specific parameters like sample size, producer's risk, consumer's risk, and termination criteria. Sampling inspection, or reliability sampling, plays a pivotal role in maintaining product quality. It involves subjecting items to testing, collecting data on their lifespans, and making acceptance or rejection decisions based on the test results. When assessing an item's quality primarily based on its lifespan, which can be suitably described using a continuous probability distribution; such a plan is termed a "life test sampling plan." This article explores the application of the Exponential Rayleigh distribution within the realm of reliability sampling plans, emphasizing the utilization of hybrid censoring for life checks and median lifetime evaluations. This approach is leveraged to formulate reliability single sampling plans applicable to the Exponential Rayleigh distribution. The article utilizes binomial probabilities to compute the parameters of these sampling plans, aiming to strike a balance between protecting the interests of both the producer and the consumer while minimizing producer risks. The study involves calculating the specified median lifetime and determining design parameters like sample size and acceptance thresholds to meet predefined quality standards. The flexibility of the Exponential Rayleigh distribution in analyzing various types of lifetime data is highlighted, owing to its scale and shape parameters. To illustrate the concepts related to sampling strategies, a numerical example is provided in the sampling strategies section of the article.

Cite: Nandhini M, Radhika A, Jeslin J, Manigandan P  A HYBRID APPROACH TO SINGLE ACCEPTANCE SAMPLING PLANS FOR LIFETIMES MODELED WITH THE EXPONENTIAL RAYLEIGH DISTRIBUTION . Reliability: Theory & Applications. 2024, March 1(77): 100-107, DOI: https://doi.org/10.24412/1932-2321-2024-177-100-107

CHARACTERIZATION OF SOME CONTINUOUS DISTRIBUTIONS BY CONDITIONAL VARIANCE OF RECORD VALUES

Zaki Anwar, Mohd Faizan, Zakir Ali

Characterization of a probability distribution gives a unique property enjoyed by that distribution. Various approaches are available in the literature to characterize distributions through record values. Many researchers have characterized Exponential, Pareto, and Power function distributions using moments, conditional expectation, and some other characteristics of record values. In this paper, we have characterized these three distributions through conditional variance of adjacent record values. The results have been verified using numerical computation.

Cite: Zaki Anwar, Mohd Faizan, Zakir Ali CHARACTERIZATION OF SOME CONTINUOUS DISTRIBUTIONS BY CONDITIONAL VARIANCE OF RECORD VALUES. Reliability: Theory & Applications. 2024, March 1(77): 108-112, DOI: https://doi.org/10.24412/1932-2321-2024-177-108-112

SOME INFERENTIAL ASPECTS ON THREE-STATION TANDEM QUEUE

Ambily Jose, Agnes Jerome, M. R. Irshad

Considered is a three-station tandem queue with service times at stations 1, 2, and 3 are exponentially distributed with customers arriving according to the Poisson process at station 1. Given that the stationary distribution is the product of three independent geometric distributions with the intensity parameters, maximum likelihood estimators and Bayes estimators of the intensity parameters based on the number of customers present at different time periods are obtained. Furthermore, the minimal posterior risk and minimum Bayes risk of the estimators are computed. Also, a simulation study is conducted to evaluate the performance of the estimators obtained.

Cite: Ambily Jose, Agnes Jerome, M. R. Irshad SOME INFERENTIAL ASPECTS ON THREE-STATION TANDEM QUEUE. Reliability: Theory & Applications. 2024, March 1(77): 113-121, DOI: https://doi.org/10.24412/1932-2321-2024-177-113-121

RELIABILITY MODELING OF A BUTTER CHURNER AND CONTINUOUS BUTTER MAKING PRODUCTION SYSTEM

Upasana Sharma, Drishti

In the dairy plant, an investigation into the machine that makes butter was subjected to a reliability study in relation to the seasonal demand. In the process of expanding the butter churner into a machine that can make butter continuously, a more reliable operational model was devised. Both the models and the data acquired with MATLAB have been subjected to availability and reliability testing and analysis. In addition, the graphical analysis was carried out with the help of Code Blocks and Excel. A comparison of the two models was then covered as the final topic. It was discovered that (a) the extended model was superior to the current model, (b) the failure rate of the existing line increased, which implies that a new machine needs to be added to the line to share the load, which results in improved production, and (c) the failure rate of the extended model was lower than the failure rate of the existing model. (c) in order to maximise profits while simultaneously minimising losses The effectiveness of the system ought to be enhanced by performing routine maintenance during both the summer and the winter.

Cite: Upasana Sharma, Drishti RELIABILITY MODELING OF A BUTTER CHURNER AND CONTINUOUS BUTTER MAKING PRODUCTION SYSTEM. Reliability: Theory & Applications. 2024, March 1(77): 122-139, DOI: https://doi.org/10.24412/1932-2321-2024-177-122-139

STREAMLINING PRODUCT DEPLOYMENT: ENHANCING EFFICIENCY THROUGH KITTING PROCESSES

G. Ayyappan, S. Sankeetha

Considering a single server with two queues that is prone to unreliability. The server offers a kitting process and performs necessary checks and rectifications when required. The arrival of items follows a Markovian arrival process, while the service is distributed based on a phase type distribution. The incoming products may exhibit issues such as poor quality or defects. If either of the queues is empty, the server is unable to provide the requested service and remains inactive. Furthermore, if all queues are empty, the server goes into a vacation mode. Breakdowns, repairs, instances of customers leaving without service (reneging), and vacation periods are all modeled using an exponential distribution. To gain insights into the performance of the queueing model, various performance metrics are analyzed and represented through 2D and 3D graphs.

Cite: G. Ayyappan, S. Sankeetha STREAMLINING PRODUCT DEPLOYMENT: ENHANCING EFFICIENCY THROUGH KITTING PROCESSES. Reliability: Theory & Applications. 2024, March 1(77): 140-159, DOI: https://doi.org/10.24412/1932-2321-2024-177-140-159

ON SOME PROPERTIES AND APPLICATIONS OF THE TYPE II HALF-LOGISTIC EXPONENTIATED FRECHET DISTRIBUTION

Olalekan Akanji Bello, Sani Ibrahim Doguwa, Abukakar Yahaya, Haruna Mohammed Jibril

As the dimensions of available data for analysis continues to grow rapidly, it becomes imperative to develop new probability distributions that can more accurately represent various phenomena. In this research paper, we introduce a novel continuous probability distribution known as the Type II Half-Logistic Exponentiated Frechet Distribution, characterized by four positive parameters. This distribution expands upon the traditional Frechet distribution by introducing two additional parameters. We derive a significant density representation for this distribution. Furthermore, we delve into several statistical and mathematical properties associated with the Type II Half-Logistic Exponentiated Frechet distribution. This includes explicit expressions for key metrics such as the quantile function, probability weighted moments, moments, moments generating function, reliability function, hazard function, and order statistics. To estimate the model parameters effectively, we employ a maximum likelihood estimation technique and present the results of a simulation study. Our research underscores the superiority of this new distribution by applying it to two real-world datasets. Notably, the findings demonstrate that the Type II Half-Logistic Exponentiated Frechet distribution outperforms other considered distributions in fitting the two real datasets.

Cite: Olalekan Akanji Bello, Sani Ibrahim Doguwa, Abukakar Yahaya, Haruna Mohammed Jibril ON SOME PROPERTIES AND APPLICATIONS OF THE TYPE II HALF-LOGISTIC EXPONENTIATED FRECHET DISTRIBUTION . Reliability: Theory & Applications. 2024, March 1(77): 160-174, DOI: https://doi.org/10.24412/1932-2321-2024-177-160-174

.AVAILABILITY OPTIMIZATION OF A PAINT MANUFACTURING PLANT USING GREY WOLF OPTIMIZATION: A METAHEURISTIC APPROACH

Ashish Kumar, Vijay Singh Maan, Monika Saini

The primary objective of present research work is to evaluate and improve the performance and availability of the paint manufacturing plant. Paint manufacturing plant consists of five subsystem naming mixer, grinder, thinner, labelling, and filling unit. Among them labelling and filling unit have two machines in parallel configuration and both are working simultaneously. All failure and repair rates are distributed exponentially. Markov birth-death process is utilized to model the dynamic behavior of the system and its sub-components, enabling a quantitative analysis of system availability. Grey wolf optimization (GWO), a swarm-based optimization technique is used to optimize the availability of the system. Moreover, the research conducts a thorough comparison between the outcomes derived from the Markov birth-death process and the GWO technique. By harnessing the power of GWO, the study aims to further enhance the plant's overall performance.

Cite: Ashish Kumar, Vijay Singh Maan, Monika Saini .AVAILABILITY OPTIMIZATION OF A PAINT MANUFACTURING PLANT USING GREY WOLF OPTIMIZATION: A METAHEURISTIC APPROACH . Reliability: Theory & Applications. 2024, March 1(77): 175-182, DOI: https://doi.org/10.24412/1932-2321-2024-177-175-182

DESIGNING AND EVALUATION OF SKIP-LOT SAMPLING PLAN OF TYPE SkSP-T WITH SINGLE SAMPLING PLAN AS REFERENCE PLAN UNDER THE CONDITION OF INTERVENED POISSON DISTRIBUTION

S. Suganya, K. Pradeepa Veerakumari

This paper describes the scheming technique of new system of skip lot sampling plan of type SkSP-T with Single Sampling Plan as Reference plan under the condition of Intervened Poisson Distribution. The designing methodology includes the evaluation of Acceptable Quality Level, Limiting Quality Level, Operating Ratio, and Operating Characteristic curves. Tables are simulated by changing various parametric values of SkSP-T, SSP and IPD and operating characteristic curves are drawn by using R language.

Cite: S. Suganya, K. Pradeepa Veerakumari  DESIGNING AND EVALUATION OF SKIP-LOT SAMPLING PLAN OF TYPE SkSP-T WITH SINGLE SAMPLING PLAN AS REFERENCE PLAN UNDER THE CONDITION OF INTERVENED POISSON DISTRIBUTION . Reliability: Theory & Applications. 2024, March 1(77): 183-190, DOI: https://doi.org/10.24412/1932-2321-2024-177-183-190

EJAZ DISTRIBUTION A NEW TWO PARAMETRIC DISTRIBUTION FOR MODELLING DATA

Aijaz Ahmad, M. A. Lone, Aafaq. A. Rather

This paper introduces a novel probability distribution known as the Ejaz distribution (ED), which is characterized by two parameters. The study offers a comprehensive analysis of this distribution, including an examination of key properties such as moments, moment-generating functions, order statistics, and reliability functions. Additionally, the paper explores the graphical representation of essential functions like the probability density function, cumulative distribution function, and hazard rate function, enhancing our visual understanding of their behavior. The distribution’s parameters are estimated using the widely accepted method of maximum likelihood estimation. Through real-world examples, the paper highlights the practical applicability of the Ejaz distribution, demonstrating its performance and relevance in diverse scenarios.

Cite: Aijaz Ahmad, M. A. Lone, Aafaq. A. Rather EJAZ DISTRIBUTION A NEW TWO PARAMETRIC DISTRIBUTION FOR MODELLING DATA. Reliability: Theory & Applications. 2024, March 1(77): 191-201, DOI: https://doi.org/10.24412/1932-2321-2024-177-191-201

RELIABILITY INVESTIGATION OF THE SPIRULINA PRODUCTION PLANT USING GUMBEL-HOUGAARD FAMILY COPULA

Priya Chaudhary, Shikha Bansal

This study examines the consistency metrics used to evaluate the durability of a spirulina production plant, which consists of seven subsystems: cultivation pond, paddlewheel, filter unit, washing unit, spray dryer, ribbon blender, and packaging. By studying the spirulina firm, we can repair it by discovering future failures. We can increase spirulina production so that untimely failure can be prevented and production can be increased. There are two types of system failures: partial and total. While a full failure renders the system incapable of operating, a partial failure is thought to degrade the system. In contrast, repair rates follow two different types of distributions: an ordinary and an exponential distribution. The system in a partially failed or degraded condition is thought to be repaired using general time distribution. In contrast, fully failed systems are thought to be fixed using the Gumbel-Hougaard family copula distribution. Using the supplementary variable approach, the system is examined. A Chapmen-Kolmogorov differential equation is created and solved by applying the Gumbel-Haugaard family Copula approach, employing the schematic representation of the system's state. supplementary variable approaches are applied to develop and resolve the differential equations related to transition diagrams, which are significant to this research. Reliability, availability, profitability, and MTTF are the critical performance metrics for the spirulina production plant. Moreover, sensitivity analysis is carried out for MTTF.

Cite: Priya Chaudhary, Shikha Bansal  RELIABILITY INVESTIGATION OF THE SPIRULINA PRODUCTION PLANT USING GUMBEL-HOUGAARD FAMILY COPULA . Reliability: Theory & Applications. 2024, March 1(77): 202-216, DOI: https://doi.org/10.24412/1932-2321-2024-177-202-216

EFFICIENT FRAMEWORK OF SECURITY FOR INTERNET OF THINGS

Dr. Mihir Mehta, Dr. Kajal Patel, Dr. Komal Anadkat

IoT security represents a highly compelling subject of research at present. The absence of a viable security solution for IoT applications could render them ineffective across various domains such as healthcare, smart homes, inventory management, smart agriculture, and more. Within the IoT architecture, security services like Confidentiality, Integrity, and Authentication play pivotal roles. In our research, we have concentrated on the Authentication service, which is fundamental for distinguishing users and devices unequivocally within a network. Authentication serves as the initial and crucial step in establishing secure communications among diverse IoT devices and users within the network. A compromised Authentication service could open the door for unauthorized users or devices to infiltrate the network, potentially leading to harmful activities like Masquerade attacks, Man-in-the-Middle (MITM) attacks, and Replay attacks.Currently, Authentication stands as a widely adopted and essential method for granting access to devices within IoT networks. Our contribution involves the development of a Multi-factor IoT Authentication Model, leveraging two key parameters: Device Context Information and Dynamic Key-based authentication.Our proposed approach begins by verifying the origin of information. If the origin is deemed valid, our model proceeds to validate the identity of the device. In the event of an intruder attempting to manipulate the device's origin from its predefined context to an alternative location, our system can swiftly detect this deviation, thereby enabling the rejection of communication requests from compromised devices.Following the verification of context information, we initiate mutual authentication between the IoT device and the server, employing the Challenge-response model. As a result of this second step, individual Session keys are generated at both the device and server sides, facilitating secure communication within a specific time window.

Cite: Dr. Mihir Mehta, Dr. Kajal Patel, Dr. Komal Anadkat EFFICIENT FRAMEWORK OF SECURITY FOR INTERNET OF THINGS . Reliability: Theory & Applications. 2024, March 1(77): 217-227, DOI: https://doi.org/10.24412/1932-2321-2024-177-217-227

M/M/∞ QUEUE WITH IMPATIENT CUSTOMERS

Gulab Singh Bura

In this paper we proposed an M/M/∞ queue with impatient customers. Generally, customers are impatient due to long waits in queue but in this work, we consider the case when customers are not impatient due to long waits but they are impatient due to the poor quality of service. We model and analyze this queueing system by using continued fraction technique and obtained the probability mass function of the customers present in the system in time dependent form. Also, we calculate the average queue size. Finally, some graphical representations are given to illustrate the model.

Cite: Gulab Singh Bura M/M/∞ QUEUE WITH IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2024, March 1(77): 228-237, DOI: https://doi.org/10.24412/1932-2321-2024-177-228-237

REGULARITY OF ALTERNATE QUADRA SUBMERGING POLAR FUZZY GRAPH AND ITS APPLICATION

Anthoni Amali A, J. Jesintha Rosline

Fuzzy soft sets and graphs are invented to solve uncertain problems in the field of Applied mathematics. It is a general mathematical tool introduced with many parameters to model the vagueness of the changing world. The insight learning of the AQSP fuzzy soft graphs paved the way to discover the extension of the AQSP fuzzy soft graph. In this research article we introduce the Regularity of AQSP fuzzy soft graph with definitions, theorems, properties, and real-life applications. The aim of this invention is mainly to obtain the parametric values in submerging level of confidence [-0.5, 0.5]   [-1,1]. The scope of this new AQSP fuzzy soft graph is to solve the imprecise problems in the field of Mathematical Engineering, Bio Mathematics, Economics, Medical Science, Artificial Intelligence and Machine learning. The regularity of AQSP fuzzy soft graph is combined with the concepts of regular, totally regular, and perfectly regular. The application of this new graph is developed for governing of the women safety vehicle network in different spots with membership submerging values. The future extension can be applied in Approximate reasoning, Mathematical psychology, Decision making for medical diagnosis.

Cite: Anthoni Amali A, J. Jesintha Rosline REGULARITY OF ALTERNATE QUADRA SUBMERGING POLAR FUZZY GRAPH AND ITS APPLICATION. Reliability: Theory & Applications. 2024, March 1(77): 238-253, DOI: https://doi.org/10.24412/1932-2321-2024-177-238-253

STATISTICAL ANALYSIS OF SPLIT-PLOT DESIGN USING SPECIAL TYPE OF GRAPHS

V. Saranya, S. Kavitha, M. Pachamuthu, S. Vijayan

When all experimental runs cannot be done under homogeneous conditions, blocking can be utilized to increase the power for testing treatment effects. In many real-life environments, there is at least one factor that is hard to change, leading to a split-plot structure. This paper demonstrates how to generate certain graphs using main-plot and sub-plot analyses, as well as providing a catalog. As a result, during situations where the candidate set is too huge to be tractable, the design of split-plot experiments becomes computationally feasible. The designs were considered ideal because they were capable and efficient in estimating the fixed effects of the suitable statistical model given the split-plot design structure. The Split-Plot Design (SPD) is the complete block design which plays an important role in the fields of agriculture, medicine, and industries. This SPD is specifically suited for a two-factor experiment that has more treatments than can be accommodated by a complete block design. In an SPD, one factor is assigned to the main- plot. The assigned first factor is called the main - plot factor. The main- plot is then divided into subplots and the second factor is called the sub - plot factor. SPD is most used for (i) few experimental materials may be rare while the other experimental materials may be available in large quantity, (ii) the levels of one or more treatment factor or easy to change and the alteration of levels of other treatment factors are costly or time-consuming. Given the extensive study done in graph theory, it has developed to be a very broad subject in mathematics. Graphs are important because they are a visual way of expressing information. A graph shows data that is equivalent to many words. A graph can convey information that is difficult to express in words. A bipartite graph is a type of graph in which the entire graph may be divided into two bipartite sets, with edges connecting vertices in one set to vertices in the other. Vertex coloring is the procedure of assigning labels or colors to each vertex in a graph. The data set was also manually analyzed to validate the software-analyzed outcomes. R gave the same results as the manual analysis, showing that they were both correct. R is mainly command-based. The proposed approach is demonstrated using agricultural and industrial examples.

Cite: V. Saranya, S. Kavitha, M. Pachamuthu, S. Vijayan  STATISTICAL ANALYSIS OF SPLIT-PLOT DESIGN USING SPECIAL TYPE OF GRAPHS . Reliability: Theory & Applications. 2024, March 1(77): 254-267, DOI: https://doi.org/10.24412/1932-2321-2024-177-254-267

INFERENCE ON THE TIME-DEPENDENT STRESS-STRENGTH RELIABILITY MODELS BASED ON FINITE MIXTURE MODELS

Krishnendu K., Annie Sabitha Paul, Drisya M., Joby K. Jose

Time-dependent stress-strength reliability engages with the chance of survival for systems with dynamic strength and/or dynamic stress. When a system is allowed to run continuously, each run will cause a change in the strength of the system. The repeated occurrence of stress on the system over each run will affect the survival capacity of the system. In this paper, we consider the distribution of time taken for the completion of a run by the system follows gamma and the stress or strength of the system follows a finite mixture of lifetime probability models. Here we consider two cases in which the first case deals with stress and strength following a finite mixture of Weibull distribution and in the second case the stress and strength is assumed to follow a finite mixture of the power-transformed half-logistic distribution. Moreover, the strength of the system is assumed to decrease by a constant and the stress acting on the system is assumed to increase by a constant over each run. We obtained the expression of the stress-strength reliability function and explained the ML and Bayesian methods for the estimation of the reliability at various time points.

Cite: Krishnendu K., Annie Sabitha Paul, Drisya M., Joby K. Jose INFERENCE ON THE TIME-DEPENDENT STRESS-STRENGTH RELIABILITY MODELS BASED ON FINITE MIXTURE MODELS. Reliability: Theory & Applications. 2024, March 1(77): 268-284, DOI: https://doi.org/10.24412/1932-2321-2024-177-268-284

DUAL EXPONENTIAL RATIO ESTIMATOR IN PRESENCE OF NON-RESPONSE

Rafia Jan, T. R. Jan and Faizan Danish

The manuscript under consideration delves into a comprehensive exploration of the dual exponential ratio estimator, particularly in the context of non-response scenarios. In the following discourse, we will embark on an intricate journey through this research, emphasizing the pivotal aspects and findings that unravel the significance of this estimator in the realm of statistical estimation. The crux of this investigation revolves around evaluating the Mean Squared Error (MSE) and the Predictive Relative Efficiency (PRE) of the dual exponential ratio estimator. These two performance metrics serve as essential benchmarks for assessing the accuracy and effectiveness of the estimator. Notably, they play a crucial role in determining the estimator's suitability for practical applications, especially in situations where non-response is prevalent. To begin our exploration, it is imperative to understand the fundamental concept of the dual exponential ratio estimator. This estimator is a statistical tool employed in situations where traditional estimators may falter due to non-response, a phenomenon frequently encountered in surveys and data collection. It leverages a dual exponential model to address this challenge, making it a valuable addition to the toolkit of statisticians and researchers. The manuscript embarks on a rigorous theoretical analysis of the dual exponential ratio estimator's MSE and PRE. Through a series of mathematical derivations and proofs, the authors elucidate the underlying principles governing its performance. This theoretical foundation is crucial, as it not only establishes a solid framework for evaluating the estimator but also provides insights into its behavior under different conditions. However, theory alone can only take us so far. To validate the theoretical findings and assess the estimator's practical utility, numerical experiments are conducted. These experiments involve simulations and real-world data scenarios, allowing the authors to draw comparisons between the dual exponential ratio estimator and traditional estimators. The numerical results serve as a bridge between theory and application, offering empirical evidence of the estimator's prowess. In essence, this manuscript fills a critical gap in the field of statistical estimation by thoroughly investigating the dual exponential ratio estimator's performance in the presence of non-response. By juxtaposing its MSE and PRE with those of traditional estimators, it provides valuable insights into the potential advantages of adopting this novel approach. Moreover, the combination of rigorous theory and practical validation ensures that the findings are both intellectually sound and operationally relevant. The dual exponential ratio estimator, as explored and analyzed within these pages, emerges as a promising solution, backed by both theoretical rigor and empirical support. This research contributes not only to the theoretical foundations of statistics but also to its real-world applications, underscoring the estimator's potential to enhance the accuracy and reliability of estimation in the face of non-response complexities.

Cite: Rafia Jan, T. R. Jan and Faizan Danish DUAL EXPONENTIAL RATIO ESTIMATOR IN PRESENCE OF NON-RESPONSE. Reliability: Theory & Applications. 2024, March 1(77): 285-296, DOI: https://doi.org/10.24412/1932-2321-2024-177-285-296

PROCESS CAPABILITY ANALYSIS FOR NON NORMAL DATA BASED ON BOX-COX TRANSFORMATION THROUGH TESTS OF GOODNESS OF FIT

J. Krishnan, R. Vijayaraghavan

Process capability analysis is an effective and efficient tool for quality assurance. When the distribution of the underlying quality characteristics is not normal, modifications of the basic process capability indices are required. Literature in process control provides avenues to resolve the issue of non-normality and data transformation is one of the approaches frequently applied in practice. Primarily the Box – Cox transformation (BCT) is employed to transform the non normal data into normal data which originally utilizes the method of maximum likelihood estimation (MLE) to find the single transformation parameter λ. There are alternative methods to estimate the optimal parametric value λ using goodness of fit tests rather using MLE method. In order to bring improved estimates, this paper makes a fresh attempt to estimate process capability analysis (PCA) using transformed data through different goodness of fit tests. The simulation study uses variety of asymmetric behaviors from a Weibull distribution generating a random sample of 100 data points to find the best goodness of fit test for better process capability estimates that are compared to the standard of six sigma results for non-normal data. Final result shows that Shapiro-Wilk's (SW) and Artificial Covariate (AC) methods are performing well when compared to the method of MLE. Minitab software and R programming language were utilized for data simulation and analysis.

Cite: J. Krishnan, R. Vijayaraghavan  PROCESS CAPABILITY ANALYSIS FOR NON NORMAL DATA BASED ON BOX-COX TRANSFORMATION THROUGH TESTS OF GOODNESS OF FIT . Reliability: Theory & Applications. 2024, March 1(77): 297-309, DOI: https://doi.org/10.24412/1932-2321-2024-177-297-309

THE USE OF EXPERIMENTAL MODELLING IN THE PREDICTION OF PRODUCT RELIABILITY

Alena Breznická, Pavol Mikuš

When designing new systems and components, it is very important to correctly determine the degree and ability of the joint to withstand stress and load. Every new product that is intended for the market must meet the requirements for high safety and reliability during the entire life cycle. The presented article deals with the possibility of modelling the ability to withstand such a load, the principle of the interference method was used in the experimental modelling. The interference theory of reliability is based on the analysis of regularities and properties of two random variables that characterize reliability. Among these elementary properties from the point of view of reliability assessment, we can successfully use dependability and lifetime analysis. It originates from the concept of "safe life", which is deterministic, based on determining and respecting the values of reliability factors. The described approach assumes that a malfunction or a faulty function occurs when the strength limit of the object is exceeded, i.e., ability to withstand stress.

Cite: Alena Breznická, Pavol Mikuš  THE USE OF EXPERIMENTAL MODELLING IN THE PREDICTION OF PRODUCT RELIABILITY . Reliability: Theory & Applications. 2024, March 1(77): 310-319, DOI: https://doi.org/10.24412/1932-2321-2024-177-310-319

A STUDY ON PARTIALLY ACCELERATED LIFE TEST MODEL FOR GENERALIZED INVERSE RAYLEIGH DISTRIBUTION UNDER ADAPTIVE TYPE-II PROGRESSIVE HYBRID CENSORING

Intekhab Alam, Trapty Agarwal, Awakash Mishra, Aanchal Gaba

Modeling and examination of lifetime phenomena are the main aspects of statistical work in a wide variety of scientific and industrial areas. The area of lifetime information analysis has developed and extended quickly with respect to methodology, theory, and fields of applications. The point and interval maximum-likelihood estimations of generalized inverse Rayleigh distribution (GIRD) parameters and the acceleration factor are considered in this work. The estimation procedure is carried out for a partially accelerated step-stress model under adaptive Type-II progressive hybrid censored data. The biases and the mean square errors of the maximum-likelihood estimators are computed to assess their performances in the occurrence of censoring developed in this study through a Monte Carlo simulation study.

Cite: Intekhab Alam, Trapty Agarwal, Awakash Mishra, Aanchal Gaba A STUDY ON PARTIALLY ACCELERATED LIFE TEST MODEL FOR GENERALIZED INVERSE RAYLEIGH DISTRIBUTION UNDER ADAPTIVE TYPE-II PROGRESSIVE HYBRID CENSORING. Reliability: Theory & Applications. 2024, March 1(77): 320-334, DOI: https://doi.org/10.24412/1932-2321-2024-177-320-334

EFFECT OF CLASSICAL AND ROBUST REGRESSION ESTIMATORS IN THE CONTEXT OF HIGHDIMENSIONAL DATA WITH MULTICOLLINEARITY AND OUTLIERS

Muthukrishnan R, Karthika Ramakrishnan

Regression methods are used for the estimation and prediction in various fields of statistical study. It is a statistical method commonly used for determining the degree of relationship between a response and a number of explanatory variables. These explanatory variables may correlate each other and lead to multicollinearity. More than two predictor variables with high correlation show the existence of multicollinearity which results in the estimator having a high variance. Ordinary Least Square estimation fails to give a better regression estimator, when the model's presumptions are not met. This paper explores the various methods which can tolerate the problems of multicollinearity and outliers. This study compares different types of regression estimators such as Ordinary Least Square, Robust, Ridge, and Liu by computing various error values such as Mean Absolute Error, Root Mean Square Error, Mean Absolute Percentage Error and R2 under real environment that has both multicollinearity and outliers. To compare the fit of the aforementioned regression models, the Akaike Information Criterion was also calculated. According to the error measures and AIC this study concludes that the Liu regression estimator performs well when compared with the other estimation methods.

Cite: Muthukrishnan R, Karthika Ramakrishnan EFFECT OF CLASSICAL AND ROBUST REGRESSION ESTIMATORS IN THE CONTEXT OF HIGHDIMENSIONAL DATA WITH MULTICOLLINEARITY AND OUTLIERS. Reliability: Theory & Applications. 2024, March 1(77): 335-341, DOI: https://doi.org/10.24412/1932-2321-2024-177-335-341

EXPONENTIATED WEIBULL DISTRIBUTION: BAYESIAN ESTIMATION USING PROGRESSIVE TYPE I INTERVAL CENSORING

M. Kumar, K P Aswathi

A three-parameter distribution known as the Generalized Weibull (GW) or Exponentiated Weibull distribution is studied in this work. We construct Baye’s estimators for the unknown parameters and present reliability function using progressive type I interval censoring data. Two different loss functions, namely, squared error loss and general entropy loss functions are applied to derive Baye’s estimators. It is observed that there is no closed-form solution for Baye’s estimators as well as for MLE. Hence, Lindley’s approximation procedure is applied to obtain Bayesian estimator of unknown parameters, and Newton Rapson method is employed to obtain MLE’s numerically. The corresponding reliability function is derived. Monte Carlo simulation is used to obtain MLE. Further, the performance of MLE and Bayes estimators are compared in terms of their respective MSE and Relative errors. It is noted by numerical computation that MLE’s performs better than Bayes estimators. In addition to this, Bayes estimators obtained using Squared error loss function and general entropy loss function are compared. It is observed through numerical computation that general entropy loss function is better in terms of MSE.

Cite: M. Kumar, K P Aswathi EXPONENTIATED WEIBULL DISTRIBUTION: BAYESIAN ESTIMATION USING PROGRESSIVE TYPE I INTERVAL CENSORING. Reliability: Theory & Applications. 2024, March 1(77): 342-359, DOI: https://doi.org/10.24412/1932-2321-2024-177-342-359

METHODS FOR ENSURING AND PROVING FUNCTIONAL SAFETY OF AUTOMATIC TRAIN OPERATION SYSTEMS

I.B. Shubinsky, E.N. Rozenberg, H. Schäbe

The paper examines the specificity of artificial intelligence-based automatic train operation systems. Justifying the functional safety (FS) of such systems is quite difficult. The paper proposes a process for proving the functional safety of intelligent systems. A hybrid control system for a shunting locomotive was developed and analysed. It combines machine vision (MV), train protection devices and manual control by a driver. A model is presented that allows examining the functional safety of a locomotive control system layer by layer, i.e., evaluating the time to safety degradation depending on the component failure and subsequent requirement of bringing the locomotive to a complete stop. This allows to improve the FS of the shunting locomotive control system with machine vision from SIL 2 to SIL 3 and maintaining it during sufficiently long periods of time (over a quarter of the mean time to system failure). The mean time of faultless operation of a locomotive control system until it has to be brought to a complete stop for safety reasons can be increased three times. A general approach is proposed to design the functional safety of automatic train operation systems. It is based on the division of the information processing process into two subprocesses, i.e., internal intelligent information processing onboard the locomotive for the purpose of decision-making regarding track vacancy and communication of initial visual information to the operating driver for decision-making. The division of this process must be combined with redundant machine vision facilities, regular comparison of the outputs of the onboard and fixed machine vision facilities, redundant comparison outputs, smoothing of the outputs in the process of locomotive movement.

Cite: I.B. Shubinsky, E.N. Rozenberg, H. Schäbe METHODS FOR ENSURING AND PROVING FUNCTIONAL SAFETY OF AUTOMATIC TRAIN OPERATION SYSTEMS. Reliability: Theory & Applications. 2024, March 1(77): 360-375, DOI: https://doi.org/10.24412/1932-2321-2024-177-360-375

SENSITIVITY AND PROFITABILITY ANALYSIS OF TWO-UNITS AMMONIA/UREA PLANT

Sara Salim A Oraimi, Syed Mohd Rizwan, Kajal Sachdeva

This paper presents a reliability modelling of a two-unit ammonia/urea plant. Real maintenance data of the production plant have been used for this purpose. Four types of failure were noted: process, electrical, mechanical and instrumental failures. Both ammonia/urea formation units work in parallel and do not fail simultaneously. Various reliability indices of the plant, such as availability, busy period for repair, and expected number of repairs for each type of failure, have been obtained. Markov processes and regenerative point techniques are used for analysis. Profit analysis for the plant is also done, along with a graphical representation of various parameters. Finally, sensitivity analysis is carried out to see the impact of varied parameters on the profit function of the plant.

Cite: Sara Salim A Oraimi, Syed Mohd Rizwan, Kajal Sachdeva SENSITIVITY AND PROFITABILITY ANALYSIS OF TWO-UNITS AMMONIA/UREA PLANT. Reliability: Theory & Applications. 2024, March 1(77): 376-386, DOI: https://doi.org/10.24412/1932-2321-2024-177-376-386

STUDIES ON A NEW MANPOWER MODEL WITH NONHOMOGENEOUS POISSON RECRUITMENT, PROMOTION AND LEAVING PROCESSES

K. Suryanarayana Rao, K. Srinivasa Rao

For proper utilization of manpower in any organization manpower modeling is needed. This paper addresses the two graded manpower model with non-stationary recruitment, promotion and leaving processes. Here it is assumed that the recruitment process in the first grade follows a NHP process which is further assumed that the promotion and leaving processes are also NHP processes. Using the difference-differential equations, the joint p.g.f of the number of employees in the organization at any time ‘t’ is derived. The characteristics of the model such as the average number of employees in each grade, the average waiting time of an employee in each grade, the variance of the number of employees in each grade and the C.V of an employee in each grade are derived explicitly. The sensitivity analysis of the model with respect to the changes in parameter is also studied through numerical illustration. The comparative study between homogeneous Poisson recruitment and NHP recruitment is also discussed. This model also improves some of the earlier models as particular cases.

Cite: K. Suryanarayana Rao, K. Srinivasa Rao STUDIES ON A NEW MANPOWER MODEL WITH NONHOMOGENEOUS POISSON RECRUITMENT, PROMOTION AND LEAVING PROCESSES. Reliability: Theory & Applications. 2024, March 1(77): 387-405, DOI: https://doi.org/10.24412/1932-2321-2024-177-387-405

THE ROLE OF RECORD VALUES IN STATISTICAL INFERENCE: A REVIEW ARTICLE

Mahmoud A. Selim Alsanea

The record values data have received the attention of researchers in statistics for over seven decades. Through these decades the records have played a significant and widely utilized role for statistical inference in parameter estimation, predicting future values, hypothesis tests, as well as stress-strength tests, and characterizing distributions. In this paper, the types of record values, some distributional properties, and statistical inferences of record values and their applications are reviewed. The purpose of this paper is to shed light on the role of record values in statistical inference. Therefore, we will examine this issue from two perspectives, the first perspective being estimation and the second perspective being prediction. These are through some of the most important lifetime distributions are Exponential, Weibull, Gumbel, Geometric, Pareto, Generalized exponential, Rayleigh, Lomax, and Nadarajah-Haghighi distributions. I hope that the findings of this paper will be useful for researchers in various fields and lead to further enhancement of research in record values theory and its applications.

Cite: Mahmoud A. Selim Alsanea  THE ROLE OF RECORD VALUES IN STATISTICAL INFERENCE: A REVIEW ARTICLE . Reliability: Theory & Applications. 2024, March 1(77): 406-423, DOI: https://doi.org/10.24412/1932-2321-2024-177-406-423

APPLICATION OF THE FUZZY-SET THEORY TO ASSESS THE KNOWLEDGE OF ELECTRIC POWER INDUSTRY SPECIALISTS

V.Kh. Nasibov R.R. Alizade I.Y. Mastaliyev A.M. Ramazanli

In most cases, the assessment of the knowledge of electric power industry workers is carried out according to a test scheme, where the correct answer is selected from the list of answers. All questions have the same difficulty and only the single correct answer gives a certain score. The article developed a universal model for assessing the knowledge of electric power industry workers, where using the theory of fuzzy logic and fuzzy inference, both the complexity of questions and the possibility of a partial correct answer are taken into account.

Cite: V.Kh. Nasibov R.R. Alizade I.Y. Mastaliyev A.M. Ramazanli  APPLICATION OF THE FUZZY-SET THEORY TO ASSESS THE KNOWLEDGE OF ELECTRIC POWER INDUSTRY SPECIALISTS . Reliability: Theory & Applications. 2024, March 1(77): 424-430, DOI: https://doi.org/10.24412/1932-2321-2024-177-424-430

A CRITICAL LITERATURE REVIEW AND FUTURE PERSPECTIVE OF RAM APPROACHES FOR COMPLEX SYSTEMS IN VARIOUS PROCESS INDUSTRIES

Mausoof Sheikh, Dr. P.C. Tewari

In the industrial systems there is a requirement that systems should work efficiently for long time. System performance is an important aspect for failure free operation but in real practice complete failure free operation of any production system is seldom possible. Detailed critical literature review for the past thirty-three years of Reliability, Maintainability and Availability (RAM) approaches has been carried out which can help to improve performance of Complex systems. Review of some papers provided the detailed information about past and current scenario of RAM practices in research field and industries. Different RAM tools and techniques extracted from the review may be helpful in qualitative and quantitative analysis of the complex systems. In this paper, author tried to focus on some major aspects of RAM approaches.

Cite: Mausoof Sheikh, Dr. P.C. Tewari  A CRITICAL LITERATURE REVIEW AND FUTURE PERSPECTIVE OF RAM APPROACHES FOR COMPLEX SYSTEMS IN VARIOUS PROCESS INDUSTRIES . Reliability: Theory & Applications. 2024, March 1(77): 431-439, DOI: https://doi.org/10.24412/1932-2321-2024-177-431-439

EXACT AND CONDITIONAL BOUNDS FOR GENERALIZED CUMULATIVE ENTROPY

Alexey V. Lebedev

The differential entropy is a natural analog of the Shannon entropy for discrete distributions in respect to absolutely continuous distributions (with density). In modern studies, many other kinds of entropy have been introduced and analyzed, including various cumulative entropies, which are based not on the density but on the (cumulative) distribution function of random variable. Such characteristics can be used, for example, in computer vision, reliability theory, risk analysis, etc. We consider some generalizations of cumulative entropy, for a wide class of entropy generators. We use the methods of probability theory, calculus of variations and Cauchy-Bunyakovsky-Schwarz inequality. In the class of centered and normalized random variables, exact and conditional bounds are found as well as the distributions on which they are attained. By conditional bounds we understand bounds for one generalized cumulative entropy given the value of another entropy (in the class of random variables with zero mean and unit variance). This problem is analogous to the previously posed and partly solved problem on conditional bounds for expectations of sample maxima when we know the expected maximum of a sample of another size or expected maxima of two smaller samples.

Cite: Alexey V. Lebedev EXACT AND CONDITIONAL BOUNDS FOR GENERALIZED CUMULATIVE ENTROPY. Reliability: Theory & Applications. 2024, March 1(77): 440-447, DOI: https://doi.org/10.24412/1932-2321-2024-177-440-447

SOME PROPERTIES OF TSALLIS ENTROPY BASED ON A DOUBLY TRUNCATED (INTERVAL) RANDOM VARIABLE

S. Jalayeria, G.R. Mohtashami Borzadarana, M. Khorashadizadehb

In this paper, we first study doubly truncated (interval) Tsallis entropy and suggest doubly truncated (interval) cumulative residual Tsallis entropy (ICRT), which is an extension of cumulative residual Tsallis entropy (CRT) and the dynamic CRT defined by the aid of Sati and Gupta and of Kumar, respectively. We investigate some properties and characterization of this measure, such as its relation with doubly truncated Shannon entropy, mean residual (past) life, and hazard rate (or reversed hazard rate). Also, the twin measure, doubly truncated (interval) cumulative past Tsallis entropy, is determined, and some of its properties are studied. Moreover, their monotonicity and related aging classes of distributions are expressed, and the upper (lower) bound for them is acquired. In the end, we propose four nonparametric estimators and compare their performance by utilizing simulation data. Also, being based on the best-proposed estimator, a real data set is additionally examined.

Cite: S. Jalayeria, G.R. Mohtashami Borzadarana, M. Khorashadizadehb SOME PROPERTIES OF TSALLIS ENTROPY BASED ON A DOUBLY TRUNCATED (INTERVAL) RANDOM VARIABLE. Reliability: Theory & Applications. 2024, March 1(77): 448-464, DOI: https://doi.org/10.24412/1932-2321-2024-177-448-464

GENERALIZED X-EXPONENTIAL BATHTUB SHAPED FAILURE RATE DISTRIBUTION AND ESTIMATION OF RELIABILITY OF MULTICOMPONENT STRESS-STRENGTH

Faryal Shabbir, Abdul Khalique

In an engineering setup, one is interested to know and determine the reliability of the system of different components. These components are usually subjected to different kinds of stress, and the reliability of the components needs to be estimated under stress. In this paper, we aim to estimate the reliability of a multicomponent stress-strength model assuming that the components of the system are working independently with a common life distribution. The system follows a comparatively new distribution named as; Generalized X-Exponential bathtub failure rate distribution. This paper studies the usefulness of this distribution in terms of estimating the maximum likelihood estimate of the reliability parameter and its asymptotic confidence intervals. Paper uses methods of parametric estimation and reliability estimation. Results are computed using Monte Carlo simulation for small samples. Real data set is presented to evaluate the performance of Generalized X Exponential Distribution (GXED) reliability estimator. Findings show that with the usage of proposed distribution, estimator of reliability parameter fits very well to the real-world situations.

Cite: Faryal Shabbir, Abdul Khalique  GENERALIZED X-EXPONENTIAL BATHTUB SHAPED FAILURE RATE DISTRIBUTION AND ESTIMATION OF RELIABILITY OF MULTICOMPONENT STRESS-STRENGTH . Reliability: Theory & Applications. 2024, March 1(77): 465-473, DOI: https://doi.org/10.24412/1932-2321-2024-177-465-473

DEVELOPMENT OF AN INTEGRATED SAFETY SISTEM FOR PRODUCTION FACILITIES: THE PROBLEM STATEMENT AND THE PROPOSED SOLUTION

Evgeny Gvozdev

The article focuses on explosion and fire hazards at production facilities of enterprises where flammable liquids and gases, categorized by explosion and fire risks, are processed, handled, transported, and stored. The goal to be attained and the tasks to be solved towards this end are formulated in the article. Consolidated areas of knowledge, accumulating results of research into risk assessment within systems of integrated safety implemented at production facilities, are considered by the author. A model for development of a novel set of research and methodological instruments (methods, techniques, software and hardware) is presented for its further practical application. The problem of developing integrated safety systems for industrial facilities, posing explosion and fire hazards, as well as the solution, are presented by the author for the first time. The novelty of the solution lies in the computation of validity of the practical application of a novel set of research and methodological instruments. A reduction in damage from accidents and fires at production facilities is demonstrated. Ultimately, the socio-economic problem of reducing damage from accidents and fires is solved not only by Russian production facilities, but also by government agencies, including the EMERCOM of Russia (Ministry of the Russian Federation for Civil Defense, Emergencies and Elimination of Consequences of Natural Disasters), Ministry of Labor and Social Protection of Russia, and Federal Environmental, Industrial and Nuclear Supervision Service of Russia.

Cite: Evgeny Gvozdev  DEVELOPMENT OF AN INTEGRATED SAFETY SISTEM FOR PRODUCTION FACILITIES: THE PROBLEM STATEMENT AND THE PROPOSED SOLUTION . Reliability: Theory & Applications. 2024, March 1(77): 474-487, DOI: https://doi.org/10.24412/1932-2321-2024-177-474-487

TRANSIENT AND METAHEURISTIC COST SCRUTINY OF MX/G(A, B)/1 RETRIAL QUEUE WITH RANDOM FAILURE UNDER EXTENDED BERNOULLI VACATION WITH IMPATIENT CUSTOMERS

Rani R, Indhira K

The transient and metaheuristic cost analysis of a MX/G(a, b)/1 retrial queue with random failure during an extended Bernoulli vacation with impatient clients is covered in this study. Any batch that arrives and discovers the server is busy, down, or on vacation joins an orbit. In the alternative, only one new customer from the group joins the service right away, while the others join the orbit. After providing each service, the server either waits to serve the following customer with probability (1 − θ) or goes on vacation with probability θ. It has been found that these systems express steady-state solutions and are dependent on time probability generating functions in consideration of their Laplace transforms. We also discuss a few exceptional and particular instances. After that, the impact of different parameters on the system’s effectiveness is evaluated. We are also talking about ANFIS. Additional approaches employed in this study to swiftly determine the system’s optimum cost include genetic algorithms (GA), artificial bee colonies (ABC), and particle swarm optimization (PSO). We also examined the graph-based convergence of several optimization algorithms.

Cite: Rani R, Indhira K TRANSIENT AND METAHEURISTIC COST SCRUTINY OF MX/G(A, B)/1 RETRIAL QUEUE WITH RANDOM FAILURE UNDER EXTENDED BERNOULLI VACATION WITH IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2024, March 1(77): 488-509, DOI: https://doi.org/10.24412/1932-2321-2024-177-488-509

REPORTING METHODOLOGY AND ALGORITHM OF MODES OF COMPLEX ENERGY SYSTEMS WITH PHASE COORDINATES

Huseyngulu Guliyev, Famil Ibrahimov

A mathematical model, algorithm and program have been developed to study any types of complex asymmetric steady-state modes and transient processes of a multi-machine power system with a renewable energy source in phase coordinates, the results of which can be used in the operational control of power system operating modes with any type of emergency automation. The developed methodology and software package can also be used in industry to check the possibility of long-term operation in the considered asymmetrical mode from the point of view of the operating conditions of the system generators and electrical receivers, to determine the need to use baluns, to select their parameters and installation locations, to ensure the efficiency of asymmetrical modes , as well as for conducting various tests and analyzing accidents that have occurred.

Cite: Huseyngulu Guliyev, Famil Ibrahimov REPORTING METHODOLOGY AND ALGORITHM OF MODES OF COMPLEX ENERGY SYSTEMS WITH PHASE COORDINATES . Reliability: Theory & Applications. 2024, March 1(77): 510-522, DOI: https://doi.org/10.24412/1932-2321-2024-177-510-522

BAYES ESTIMATION OF CAPABILITY INDEX USING THREE-PARAMETER WEIBULL DISTRIBUTION

Sonam Gubreley, Ankita Gupta, Satyanshu K.Upadhyay

The process capability index is an important tool used in quality control and process improvement. Generally, the index is estimated under the assumption of a normal distribution, although some other distributions are also recommended in the literature. This paper instead considers a three-parameter Weibull distribution and obtains an estimate of the process capability index under the Bayesian framework. Bayesian development is based on the use of non-informative priors and the posterior sample-based inferences are drawn using an important Markov chain Monte Carlo technique, namely, the Gibbs sampler algorithm. Finally, a numerical illustration based on two real datasets is provided.

Cite: Sonam Gubreley, Ankita Gupta, Satyanshu K.Upadhyay BAYES ESTIMATION OF CAPABILITY INDEX USING THREE-PARAMETER WEIBULL DISTRIBUTION. Reliability: Theory & Applications. 2024, March 1(77): 523-530, DOI: https://doi.org/10.24412/1932-2321-2024-177-523-530

A NEW ALGORITHM TO SOLVE MULTI-OBJECTIVE TRANSPORTATION PROBLEM WITH GENERALIZED TRAPEZOIDAL FUZZY NUMBERS

Ramakant Sharma, Sohan Lal Tyagi

Transportation Problem is a specific type of linear programming problem (LPP). Today, in the real world, the decision maker handles the multi-objectives at the same time. Fuzzy Concepts are used in LPP to handle the uncertainty and vagueness of data. This paper presents a new algorithm to solve a special type of fuzzy transportation problem (FTP) with the generalized trapezoidal fuzzy numbers (GTpFN) in which the decision maker is not certain about the exact value of transportation charge and the availabilities and requirements are the real numbers. In this Proposed Algorithm first, the fuzzy multi-objective transportation problem (FMOTP) is converted into a Crisp multi-objective transportation problem (MOTP) by the Proposed ranking function, and then the Crisp MOTP is transformed into a single objective transportation problem using the sum of objective functions values. The proposed algorithm gives an efficient compromise solution of FMOTP. To elaborate the proposed algorithm, one numerical example is solved.

Cite: Ramakant Sharma, Sohan Lal Tyagi A NEW ALGORITHM TO SOLVE MULTI-OBJECTIVE TRANSPORTATION PROBLEM WITH GENERALIZED TRAPEZOIDAL FUZZY NUMBERS. Reliability: Theory & Applications. 2024, March 1(77): 531-543, DOI: https://doi.org/10.24412/1932-2321-2024-177-531-543

USE OF THERMAL IMAGING METHOD OF CONTROL FOR INSPECTION OF BUILDING STRUCTURES FOR TIGHTNESS

Sofia Skachkova, Anton Avgutsevichs

In any industry related to the construction of buildings and structures we have heard about the need to assess the technical condition of various objects to assess and analyze the risks associated with the possible collapse of buildings (structures), loss of life and high costs to eliminate these consequences. Since many objects fail over time, and in general to determine the wear and tear and the possible term of further safe operation, it is necessary to conduct a technical survey. The article describes the principle of operation of thermal imaging devices for determining the reliability of building structures in residential premises, and also raises problems, the solution of which can simplify the use of thermal imaging devices in the inspection of buildings and structures and reduce the economic costs of damage compensation in case of timely detection and elimination of any defects.

Cite: Sofia Skachkova, Anton Avgutsevichs  USE OF THERMAL IMAGING METHOD OF CONTROL FOR INSPECTION OF BUILDING STRUCTURES FOR TIGHTNESS . Reliability: Theory & Applications. 2024, March 1(77): 544-550, DOI: https://doi.org/10.24412/1932-2321-2024-177-544-550

ON THE CHARACTERIZATION AND APPLICATIONS OF A THREE-PARAMETER IMPROVED WEIBULL-WEIBULL DISTRIBUTION

A. S. Mohammed, B. Abba, I. Abdullahi, Y. Zakari, A. I. Ishaq

Parametric modeling of complex lifetime data characterized with nonmonotone hazard rate (NMHR) has in recent years attract the interest of many researchers and practitioners. The three-parameter improved Weibull-Weibull distribution introduced in 2022 has demonstrated a better NMHR modeling potential in the analysis of several failure times identified with bathtub hazard rate (BHR). In this study, we present the characterization, properties and two data sets’ applications of the distribution. Various properties of the distribution obtained, include moment generating function, moments, skewness, kurtosis, and some types of entropy. Numerical results for mean, variance, skewness, and kurtosis are computed using simulation studies. Estimation of the distribution parameters is performed using the method of maximum likelihood, and the estimation method is assessed by Monte Carlo simulation experiments. The two illustrations further ascertain the capability of the model for modeling lifetime data from different scientific investigation areas.

Cite: A. S. Mohammed, B. Abba, I. Abdullahi, Y. Zakari, A. I. Ishaq ON THE CHARACTERIZATION AND APPLICATIONS OF A THREE-PARAMETER IMPROVED WEIBULL-WEIBULL DISTRIBUTION. Reliability: Theory & Applications. 2024, March 1(77): 551-563, DOI: https://doi.org/10.24412/1932-2321-2024-177-551-563

MARSHAL-OLKIN ALPHA POWER INVERSE RAYLEIGH DISTRIBUTION: PROPERTIES, ESTIMATION AND APPLICATIONS

Ismaila Olawale Adegbite, Kayode Samuel Adekeye, Olubisi Lawrence Aako

In this study, a new three-parameter distribution is introduced by extending the two-parameter Alpha Power Inverse Rayleigh distribution using Marshall-Olkin G approach. The proposed Marshall-Olkin Generalized Alpha Power Inverse Rayleigh (MOAPIR) distribution generalizes the Marshall-Olkin Inverse Rayleigh, Alpha Power Inverse Rayleigh, and Inverse Rayleigh distribution. The characterization and statistical properties of the proposed distribution such as hazard rate function, reversed hazard rate function, quantiles, moments, and order statistics were derived. The estimation of the MOAPIR distribution parameters is derived using the maximum likelihood estimation method. The performance of the proposed distribution was compared with other competing distribution using two real-life data. The goodness of fit criteria and the distribution function curve showed that the proposed distribution provides a better fit than other competing distributions of the same family of heavily positive skewed distribution.

Cite: Ismaila Olawale Adegbite, Kayode Samuel Adekeye, Olubisi Lawrence Aako MARSHAL-OLKIN ALPHA POWER INVERSE RAYLEIGH DISTRIBUTION: PROPERTIES, ESTIMATION AND APPLICATIONS . Reliability: Theory & Applications. 2024, March 1(77): 564-576, DOI: https://doi.org/10.24412/1932-2321-2024-177-564-576

ON DIFFERENT CLASSICAL ESTIMATION APPROACHES FOR TYPE I HALF LOGISTIC-TOPP-LEONE- EXPONENTIAL DISTRIBUTION

Akeem Ajibola Adepoju, Sauta S. Abdulkadir, Danjuma Jibasen

This paper aims to propose six methods of parameter estimation in order to examine the behavior of the new Type I Half Logistic Topp-leone Exponential distribution. The methods taking into consideration are Maximum Likelihood, Anderson Darling, Least Squares, Cramer von Mises, Maximum Product of Spacing, and Weighted Least Squares Methods. The results show that all the methods are consistent, since the estimates approach the true value of the parameters for all the methods. The bias, mean square error and mean relative estimates decay as the sample size is raised. The estimates of the six methods obtained for the model, indicated that MPS estimates is the closest to the true value of the parameters across the low, moderate and high sample sizes, invariable, the MPS produces the least biasness. Buttress more, the MPS produces the least MSE all through and remain the best estimator for low, moderate and high sample size of the model. Conclusively, MPS is the most consistent among the estimators for the model.

Cite: Akeem Ajibola Adepoju, Sauta S. Abdulkadir, Danjuma Jibasen ON DIFFERENT CLASSICAL ESTIMATION APPROACHES FOR TYPE I HALF LOGISTIC-TOPP-LEONE- EXPONENTIAL DISTRIBUTION . Reliability: Theory & Applications. 2024, March 1(77): 577-587, DOI: https://doi.org/10.24412/1932-2321-2024-177-577-587

ON THE Q-RAYLEIGH DISTRIBUTION AND ITS APPLICATIONS

Ibrahim Sadok

This paper introduces the two-parameter q-Rayleigh distribution, a powerful extension of the classical Rayleigh model for analysing real-world data. Compared to the Rayleigh, the q-Rayleigh incorporates a novel pathway parameter q, offering greater flexibility in capturing diverse data patterns. We delve into the mathematical properties of the q-Rayleigh, including its hazard rate function and quantile function, and explore parameter estimation through maximum likelihood methods. We demonstrate its superior fit compared to the widely-used Rayleigh distribution for real-world data. Moreover, we explore its application in reliability analysis. This comprehensive study makes the q-Rayleigh a compelling choice for modelling data exhibiting gradual transitions and enhanced flexibility.

Cite: Ibrahim Sadok ON THE Q-RAYLEIGH DISTRIBUTION AND ITS APPLICATIONS. Reliability: Theory & Applications. 2024, March 1(77): 588-602, DOI: https://doi.org/10.24412/1932-2321-2024-177-588-602

MI-K-MEAN ALGORITHM: A NEW APPROACH FOR FINANCIAL RISK ANALYSIS WITH MISSING DATA IMPUTATION IN BIG DATA

Ravindra Kumar, Diwakar Shukla, Kamlesh Kumar Pandey, Sagar, M.P.,India , Sagar, M.P., India, Amarkantak, M.P., India

The data mining is a tool of searching information from the data warehouse. Several mining algorithms exist in literature, one of the most common is the usual K-mean procedure. This generates centroids after every round of iteration. It is assumed that sample data is completely cleaned and noise free before the start of execution of the usual K-mean algorithm. If α% values are missing in sample data then after cleaning only (100-α) % values are available for the execution of the usual K-mean algorithm. Such bears a loss of information that affects the decision. This paper considers this problem and resolves such issue by replacing the missing data through imputed values calculated by the available values, called Mean Imputation (MI). It helps in financial risk analysis quite a lot because of risk prediction being taken on a larger sample (cleaned and imputed both). Several imputation procedures are available in literature. This paper considers the financial risk data as sample where the missing values of sample are imputed by the usual Mean-Imputation (MI) method and then on complete sample. Proposed MI-K-mean strategy is compared with no imputation usual procedure and found more efficient over the four-evaluation criterion of cluster formation while applying on risk data analysis.

Cite: Ravindra Kumar, Diwakar Shukla, Kamlesh Kumar Pandey, Sagar, M.P.,India , Sagar, M.P., India, Amarkantak, M.P., India  MI-K-MEAN ALGORITHM: A NEW APPROACH FOR FINANCIAL RISK ANALYSIS WITH MISSING DATA IMPUTATION IN BIG DATA . Reliability: Theory & Applications. 2024, March 1(77): 603-617, DOI: https://doi.org/10.24412/1932-2321-2024-177-603-617

A TYPE I HALF LOGISTIC TOPP-LEONE INVERSE LOMAX DISTRIBUTION WITH APPLICATIONS IN SKINFOLDS ANALYSIS

Akeem Ajibola Adepoju, Sauta S. Abdulkadir, Danjuma Jibasen, Jamiu S. Olumoh

This paper proposed a novel distribution parameterized by four parameters. This is achieved by compounding the potentials properties of the Type I half logistic topp-leone generalized distribution family with the properties of the inverse lomax distribution to form the novel Type I half logistic topp-leone inverse lomax distribution. The novel distribution is potentially capable of extending classical inverse lomax distribution. The potentiality of the shape of the probability density function of the novel distribution is worth recognizing since it produces right skewed, approximately normal, left skewed and a reverted J-shaped. Decreasing life failure shape is also observed. Distinctive features of the novel distribution such as moments, entropy, moment generating function, reliability and hazard function were derived. The estimation method explored in this study is maximum likelihood estimation. It is adopted to estimate the novel distribution unknown parameters. Real life data set was adopted to investigate the potentiality and applicability of the novel model. The type I half logistic topp-leone inverse lomax distribution outperform the recent models.

Cite: Akeem Ajibola Adepoju, Sauta S. Abdulkadir, Danjuma Jibasen, Jamiu S. Olumoh A TYPE I HALF LOGISTIC TOPP-LEONE INVERSE LOMAX DISTRIBUTION WITH APPLICATIONS IN SKINFOLDS ANALYSIS. Reliability: Theory & Applications. 2024, March 1(77): 618-630, DOI: https://doi.org/10.24412/1932-2321-2024-177-618-630

A COMPRESSIVE STUDY ON FAULT DETECTION AND DIAGNOSIS FOR RELIABLE OPERATION OF HVAC, ENERGY BUILDINGS AND MACHINERIES

M. S. Patil, G.M. Malwatkar

In Heating, Ventilation, and Air Conditioning (HVAC) systems, faults can be occurred due to various reasons such as drift deviation, valve/fan failure, water clogging, air filter obstruction, temperature sensor failure and so on. Similarly in electrical machineries faults can be occurred due to multiple causes such as phase reversal, over or under voltage, starter open/short circuit, bearing problems, insulation breakdown, overloading, thermal unbalance, environmental as well as other technical issues. The faults analysis at various stages of electrical systems are critically important for reliable operation of the system. In view of reliability and safety operations of modern sophisticated electrical systems, faults analysis and its diagnosis are necessary to avoid unaccountable losses. The faults at various stages, its causes, methods of detection and diagnosis, fault classifications are included in this work. The comment on effectiveness methods of detection of fault and diagnosis are included for electrical systems. In the industries, systems are incorporated with monitoring capacity for detection of faults at easy and early stage. This paper mainly focused on advancements in fault detection and diagnosis (FDD) methods with short review of various recent methods. This includes system information representation, methods of FDD, description of faults, fault classification, and decision actions related to maintenance, providing a systematic overview of the current state of FDD. Furthermore, the paper underscores the pivotal roles of FDD in electrical systems, emphasizing its effectiveness in identifying faulty states and taking pre-emptive actions against potential failures or accidents. The discussion extends to developments of current research in FDD approaches for electrical machineries with system monitoring, accompanied by short review of diverse and valuable FDD methodologies. The study concludes by addressing comments on recent trends, future directions, challenges, and prospective solutions in the hybrid and dynamic landscape of FDD.

Cite: M. S. Patil, G.M. Malwatkar A COMPRESSIVE STUDY ON FAULT DETECTION AND DIAGNOSIS FOR RELIABLE OPERATION OF HVAC, ENERGY BUILDINGS AND MACHINERIES. Reliability: Theory & Applications. 2024, March 1(77): 631-649, DOI: https://doi.org/10.24412/1932-2321-2024-177-631-649

M/M/C QUEUE WITH MULTIPLE WORKING VACATIONS AND SINGLE WORKING VACATION UNDER ENCOURAGED ARRIVAL WITH IMPATIENT CUSTOMERS

Prakati P, Julia Rose Mary K

This paper demonstrates an M/M/C queuing model with Multiple working vacations and also single working vacation under encouraged arrival with impatient customers. The queuing model with the servers adopting multiple working vacation policy and single working vacation are determined separately and it is observed that the servers during working vacation(s) will be serving the customers at a slower service rate when compared during regular busy period. In addition to the above conditions, if there is a rapid increase in the customers’ arrival i.e, if encouraged arrival occurs and due to this sudden growth of the queue, there may be a impatience in the behaviour of the customer. With these considerations, an M/M/C Queuing model is analysed with two vacation policies separately by applying PGF method and thus the performance measures for an M/M/C Queue with Multiple Working Vacations and Single Working Vacation under Encouraged arrival with impatient customers are evaluated.

Cite: Prakati P, Julia Rose Mary K M/M/C QUEUE WITH MULTIPLE WORKING VACATIONS AND SINGLE WORKING VACATION UNDER ENCOURAGED ARRIVAL WITH IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2024, March 1(77): 650-662, DOI: https://doi.org/10.24412/1932-2321-2024-177-650-662

BEHAVIORAL ANALYSIS AND MAINTENANCE DECISIONS OF WOOD INDUSTRIAL SUBSYSTEM USING STOCHASTIC PETRI NETS SIMULATION MODELING

Urvashi, Shikha Bansal

This study aims to optimize the productivity of the plywood manufacturing system within the wood industry. A Petri nets simulation-based technique has been used to evaluate the availability analysis of the plywood manufacturing system. A Petri nets model is created to represent the modeling of the plywood system. The model is subsequently simulated using the licensed program Petri Nets (PN) GRIF 2023.7. This simulation is used to evaluate the performance of the system. In the PN simulation model, timed transitions are fired based on the failure and repair rate of the system. Immediate transitions, on the other hand, have their own guard function for firing which is coded using a logical AND-OR gate. This study also assesses the impact of the repairman on the system’s availability. The system’s availability is optimized by increasing the number of repairmen. However, once a specific number of repairmen is reached, the system’s availability remains constant. This research is highly valuable for determining the optimal number of maintenance staff needed for the wood industrial system.

Cite: Urvashi, Shikha Bansal BEHAVIORAL ANALYSIS AND MAINTENANCE DECISIONS OF WOOD INDUSTRIAL SUBSYSTEM USING STOCHASTIC PETRI NETS SIMULATION MODELING. Reliability: Theory & Applications. 2024, March 1(77): 663-674, DOI: https://doi.org/10.24412/1932-2321-2024-177-663-674

PREDICTIVE MAINTENANCE SCHEME FOR PHASED MISSION SYSTEMS

Preeti Wanti Srivastava, Satya Rani

In both industrial and military fields, many systems are phase mission systems (PMSs) which execute mission composed of different phases in sequence. The structure, failure behaviour, and working condition of such a system may change from phase to phase. Maintenance actions comprising corrective and preventive maintenance schemes studied in the literature are aimed at retaining the maintained system in a proper condition and improving its availability and extending its life. The present paper deals with finding optimal periodic inspection time using multi-objective criteria comprising objectives of minimizing expected maintenance cost incurred due to predictive, breakdown and periodic maintenance of a PMS, and maximizing its expected residual lifetime. The predictive maintenance is condition-based preventive maintenance that anticipates system failures in order to plan timely interventions on the system and hence improve its performance. The dependency is modelled using Gumbel-Haugaard copula. An aircraft flight PMS comprising Taxiing phase, Take-Off phase, Cruising phase and Landing phase has been used to illustrate the method developed.

Cite: Preeti Wanti Srivastava, Satya Rani PREDICTIVE MAINTENANCE SCHEME FOR PHASED MISSION SYSTEMS. Reliability: Theory & Applications. 2024, March 1(77): 675-687, DOI: https://doi.org/10.24412/1932-2321-2024-177-675-687

PROFIT ANALYSIS OF REPAIRABLE JUICE PLANT

Rahul, Mohit Yadav, Hemant Kumar

Juice is a non-fermented beverage that is obtained by squeezing fruits to increase immunity. Generally, juice contains calcium, vitamin, iron, etc. to give the refresh tests. There are multiple steps to store the juice at large levels such as storing, grinding pasteurization, etc. In this paper, the performance and reliability measures of a juice plant are discussed. The juice plant has three distinct units. Unit A has washing and storage tank, unit B has grinding, blending, evaporation and pasteurization, and unit C has bottling, labeling and packing units. If any unit partially fails then the system works to a limited extent. A technician is always available to repair the failed unit. The system fails when one unit completely fails. In this paper, the failure time and repair time follow general distributions. The regenerative point graphical technique is used to explore the reliability measures.

Cite: Rahul, Mohit Yadav, Hemant Kumar PROFIT ANALYSIS OF REPAIRABLE JUICE PLANT . Reliability: Theory & Applications. 2024, March 1(77): 688-695, DOI: https://doi.org/10.24412/1932-2321-2024-177-688-695

A LITERATURE REVIEW ON DEVELOPMENT OF QUEUEING NETWORKS

V. Narmadha, P. Rajendran

This study conducts a quantitative research survey on the development of queueing networks over years. Development is a process of gradual change that takes place over many years, during which a theory slowly progress and attain a good state. Queueing theory has been through many developments which made its existence inevitable in every field. Queueing networks can be considered as a collection of nodes, where each node stands for a service facility. It has been proved to be a powerful and versatile tool for modelling facilities in manufacturing units and telecommunication networks. This paper presents the development in Queueing networks and its types over years. This paper's main objective is to give all the analysts and researchers the knowledge about the evolution that happened in Queueing networks over years.

Cite: V. Narmadha, P. Rajendran A LITERATURE REVIEW ON DEVELOPMENT OF QUEUEING NETWORKS . Reliability: Theory & Applications. 2024, March 1(77): 696-702, DOI: https://doi.org/10.24412/1932-2321-2024-177-696-702

MODELING AND ANALYSIS OF SINE POWER RAYLEIGH DISTRIBUTION: PROPERTIES AND APPLICATIONS

Aadil Ahmad Mir, S.P.Ahmad

In this manuscript, a new probability model named as Sine Power Rayleigh distribution (SPRD) is proposed using a Sine-G function as generator. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, reverse hazard rate, cumulative hazard function, mills ratio, quantile function, moments, moment generating function, conditional moments, entropy, and order statistics. The parameters of the proposed distribution were estimated using the method of maximum likelihood estimation. To assess the model’s versatility and applicability, we conduct analyses on two real life data sets. The outcomes affirm the superior performance of the newly proposed model SPRD as compared to existing models.

Cite: Aadil Ahmad Mir, S.P.Ahmad MODELING AND ANALYSIS OF SINE POWER RAYLEIGH DISTRIBUTION: PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications. 2024, March 1(77): 703-716, DOI: https://doi.org/10.24412/1932-2321-2024-177-703-716

NEW DISCRETE DISTRIBUTON FOR ZERO-INFLATED COUNT DATA

Peer Bilal Ahmad, Mohammad Kafeel Wani

Over-dispersed models are commonly utilized when the variation is more than what the model actually predicts. Since one of the reasons for over-dispersion is the large number of zeros, we employ zero-inflated models instead of more traditional ones to handle this observed occurrence. We present a zero-inflated version of a discrete distribution that was developed in 2021 in our research. Significant statistical characteristics of the suggested model have been identified, such as moments, the over-dispersion feature, generating functions, and related measures, among others. We have carried the parametric estimation using the maximum likelihood estimate. Maximum likelihood estimates are checked for usefulness in a simulation exercise. We evaluated the applicability of our developed model using three real-world data sets.

Cite: Peer Bilal Ahmad, Mohammad Kafeel Wani NEW DISCRETE DISTRIBUTON FOR ZERO-INFLATED COUNT DATA. Reliability: Theory & Applications. 2024, March 1(77): 717-728, DOI: https://doi.org/10.24412/1932-2321-2024-177-717-728

STOCHASTIC OPTIMIZATION AND RELIABILITY ANALYSIS OF MUSHROOM PLANT

Shakuntla Singla, Sonia, Poonam Panwar

In the present paper the reliability model for availability analysis of mushroom plant is developed in three sub-units like water pump, winter cold standby unit A.C., and packing machine. We assume a doctor of mushroom and workers are available who examines and repairs the elements as when we need. A mathematical model of the system is developed by using all these considerations. MTSF, Availability, server of busy period and expected number of servers visit of mushroom plant are determined with the assistance of RPGT. Graphs and tables are draw to depict the behavior of various parameters such as MTSF, Availability, server of busy period and expected number of servers visits and the effect of various parameters of the plant is analyzed when repair and failure rate both are vary and also when one of them is constant.

Cite: Shakuntla Singla, Sonia, Poonam Panwar STOCHASTIC OPTIMIZATION AND RELIABILITY ANALYSIS OF MUSHROOM PLANT . Reliability: Theory & Applications. 2024, March 1(77): 729-743, DOI: https://doi.org/10.24412/1932-2321-2024-177-729-743

NUMERICAL INVESTIGATION OF RETRIAL QUEUEING INVENTORY SYSTEM WITH A CONSTANT RETRIAL RATE, WORKING VACATION, FLUSH OUT, COLLISION AND IMPATIENT CUSTOMERS

G. Ayyappan, N. Arulmozhi

The retrial queueing inventory system with working vacation, flush out, balking, breakdown, and repair, as well as a constant retrial rate and orbital client collision are all examined in this study. We made the assumption that customers arrive through a Markovian arrival process and that they would get phase-type services from the server. The inventory is replenished using a (s, S) and (s,Q) strategy, and it is expected that the replenishment time will follow an exponential distribution. If there are zero inventory items, no customers in the orbit, or both, the server will go into working vacation mode. When a customer retries an orbit while the server is serving arriving customers, the orbital customer may collide with the arriving customer during that retry, in which case both of them will be shifted back into orbit; otherwise, the orbital customer may avoid colliding with the arriving customer and may rejoin the orbit for another retry. The number of customers in the orbit and the inventory level may be found in the steady state. A cost analysis is produced along with the establishment of various important performance measures. Moreover, some numerical examples are provided to clarify our mathematical notion.

Cite: G. Ayyappan, N. Arulmozhi NUMERICAL INVESTIGATION OF RETRIAL QUEUEING INVENTORY SYSTEM WITH A CONSTANT RETRIAL RATE, WORKING VACATION, FLUSH OUT, COLLISION AND IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2024, March 1(77): 744-763, DOI: https://doi.org/10.24412/1932-2321-2024-177-744-763

ON φ-CONHARMONICALLY FLAT LORENTZIAN PARA-KENMOTSU MANIFOLDS

I. V. Venkateswara Rao, S. Sunitha Devi, K. L. Sai Prasad

The present paper deals with a class of Lorentzian almost paracontact metric manifolds namely Lorentzian para-Kenmotsu (briefly LP-Kenmotsu) manifolds. We study and have shown that a quasiconformally flat Lorentzian para-Kenmotsu manifold is locally isomorphic with a unit sphere Sn(1). Further it is shown that an LP-Kenmotsu manifold which is φ-conharmonically flat is an η-Einstein manifold with the zero scalar curvature. At the end, we have shown that a φ-projectively flat LPKenmotsu manifold is an Einstein manifold with the scalar curvature r = n(n − 1).

Cite: I. V. Venkateswara Rao, S. Sunitha Devi, K. L. Sai Prasad ON φ-CONHARMONICALLY FLAT LORENTZIAN PARA-KENMOTSU MANIFOLDS. Reliability: Theory & Applications. 2024, March 1(77): 764-769, DOI: https://doi.org/10.24412/1932-2321-2024-177-764-769

DATA ANALYSIS AND CLASSICAL ESTIMATION METHODS OF THE BOUNDED POWER LOMAX DISTRIBUTION

Amal S. Hassan, Asma M. Khalil, Heba F. Nagy

In this work, a novel bounded three-parameter power Lomax distribution termed the unit power Lomax (UPLoD) is presented. The UPLoD is capable of handling data with left and right skewed shapes according to its probability density function. Additionally, according to the hazard rate function, the distribution may be used to analyse data containing J-shaped hazard rates. It is possible to determine some of the distribution's mathematical characteristics like moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, stress strength model, and entropy (Rényi, Havrda and Charvát, Tsallis, and Arimoto) measures. The Cramér–von Mises, weighted least squares, maximum likelihood, Anderson–Darling, maximum product of spacing, and least squares approaches are among the conventional estimating techniques that are taken into account. The performance of the resulting estimates is compared using a Monte Carlo simulation based on some precision metrics. An actual data application is presented using water capacity data, and data about the Susquehanna River's maximum flood levels to show the importance of the new distribution compared to several other known distributions.

Cite: Amal S. Hassan, Asma M. Khalil, Heba F. Nagy DATA ANALYSIS AND CLASSICAL ESTIMATION METHODS OF THE BOUNDED POWER LOMAX DISTRIBUTION . Reliability: Theory & Applications. 2024, March 1(77): 770-789, DOI: https://doi.org/10.24412/1932-2321-2024-177-770-789

LIMIT CYCLES OF LENGTH TWO IN THE RIKKER MODEL AND THEIR APPLICATION IN FISHING

Gurami Tsitsiashvili, Tatyana Shatilina, Marina Osipova, Tatyana Radchenkova

The paper investigates the limit cycle of length two in the Rikker model. It is established that the dependence of the ratio of the maximum value of the cycle to the minimum depends monotonously and almost linearly on the growth coefficient of the Rikker model. Models of the parity shift of the limit cycle of length two are constructed, which is provided by a simultaneous sharp decrease/increase in the growth coefficient. On the example of the Amur salmon in 1994 It is shown that a decrease in the growth coefficient, leading to a shift in the parity of the cycle of length two, is accompanied by a low temperature during the life cycle of pink salmon, when the pink salmon population is in a state of spawn and when the young are rolling.

Cite: Gurami Tsitsiashvili, Tatyana Shatilina, Marina Osipova, Tatyana Radchenkova LIMIT CYCLES OF LENGTH TWO IN THE RIKKER MODEL AND THEIR APPLICATION IN FISHING. Reliability: Theory & Applications. 2024, March 1(77): 790-795, DOI: https://doi.org/10.24412/1932-2321-2024-177-790-795

INFERENCE ON THE INVERSE POWER BURR-HATKE DISTRIBUTION UNDER TYPE II CENSORING

Pavitra Kumari, Vinay Kumar

There are many real-life situations, where data require probability distribution function which have decreasing or upside-down bathtub (UBT) shaped failure rate function. The inverse power burr hatke distribution consists both decreasing and UBT shaped failure rate functions. Here, we address the different estimation methods of the parameter and reliability characteristics of the inverse Pareto distribution from both classical and Bayesian approaches. We consider classical estimation procedures to estimate the unknown parameter of inverse power burr-hatke distribution, such as maximum likelihood. Also, we consider Bayesian estimation using squared error loss function based joint priors. The Monte Carlo simulations are performed to compare the performances of the obtained estimators in mean square error sense. Finally, the flexibility of the proposed distribution is illustrated empirically using one real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, inverse Pareto and Burr-Hatke distributions.

Cite: Pavitra Kumari, Vinay Kumar  INFERENCE ON THE INVERSE POWER BURR-HATKE DISTRIBUTION UNDER TYPE II CENSORING . Reliability: Theory & Applications. 2024, March 1(77): 796-803, DOI: https://doi.org/10.24412/1932-2321-2024-177-796-803

A COMPARATIVE STUDY OF INVENTORY MODELLING: DETERMINISTIC OVER STOCHASTIC APPROACH

Lalji Kumar, Pratima Singh Ghoshi, Shreyashi Saxena, Kajal Sharma

This research study provides a comprehensive comparison of two critical approaches to inventory modelling- deterministic and stochastic. The deterministic model employs traditional optimization techniques to optimize complex systems, while the stochastic model leverages Particle Swarm Optimization (PSO) simulations to tackle the challenges posed by uncertain dynamics. This approach enables us to develop effective strategies for optimizing complex systems. After conducting sensitivity analyses, it was found that the deterministic model oversimplifies demand dynamics, whereas the stochastic model more adeptly captures market uncertainties. As a result, this study suggests that businesses adopt stochastic approaches to inventory management to better engage in adaptive decision-making, contingency planning, optimal resource allocation, risk mitigation, and realistic performance metrics. The research provides valuable insights for businesses seeking to navigate the complexities of modern supply chains.

Cite: Lalji Kumar, Pratima Singh Ghoshi, Shreyashi Saxena, Kajal Sharma  A COMPARATIVE STUDY OF INVENTORY MODELLING: DETERMINISTIC OVER STOCHASTIC APPROACH . Reliability: Theory & Applications. 2024, March 1(77): 804-818, DOI: https://doi.org/10.24412/1932-2321-2024-177-804-818

SEQUENTIAL TESTING PROCEDURE FOR THE PARAMETERS OF INVERSE DISTRIBUTION FAMILY

K. S. Chauhan, A. Sharma

The sequential probability ratio test is a powerful statistical tool that is frequently employed for hypothesis testing, parameter estimation, and statistical inference. The aspect of robustness is of utmost importance when employing SPRTS in practical applications. Past studies have investigated the robustness of SPRTS for specific distributions. We have developed SPRTS for a family of inverse distributions that includes eleven distinct distributions. The primary objective of this study is to investigate and evaluate the robustness of SPRTS under various conditions and distributions, focusing on the parameters of the inverse distribution family. SPRTS efficacy is measured using OC and ASN functions. This study comprehensively covers the construction and rigorous evaluation of SPRTS, particularly in testing simple null hypotheses against simple alternative hypotheses. Additionally, we investigate the robustness of SPRTS under various factors, including the presence of other parameters and specified coefficients of variation. Conclusive results, graphic representations, tables, and acceptance and rejection regions add clarity to the findings.

Cite: K. S. Chauhan, A. Sharma SEQUENTIAL TESTING PROCEDURE FOR THE PARAMETERS OF INVERSE DISTRIBUTION FAMILY. Reliability: Theory & Applications. 2024, March 1(77): 819-831, DOI: https://doi.org/10.24412/1932-2321-2024-177-819-831

CONFIDENCE INTERVAL USING MAXIMUM LIKELIHOOD ESTIMATION FOR THE PARAMETERS OF POISSON TYPE RAYLEIGH CLASS MODEL

Rajesh Singh, Preeti A. Badge, Pritee Singh

In this research paper, confidence interval using maximum likelihood estimation is obtained for Poisson type Rayleigh class for the parameters. The failure intensity function, mean time to failure function and likelihood function for the parameter is derived. Confidence interval has been obtained for the parameters using maximum likelihood estimation. To study the performance of proposed Confidence interval, average length and coverage probability are calculated by using Monte Carlo simulation technique. From the obtained intervals, it is concluded that Confidence interval for the parameters perform better for appropriate choice of execution time and certain values of parameters.

Cite: Rajesh Singh, Preeti A. Badge, Pritee Singh CONFIDENCE INTERVAL USING MAXIMUM LIKELIHOOD ESTIMATION FOR THE PARAMETERS OF POISSON TYPE RAYLEIGH CLASS MODEL. Reliability: Theory & Applications. 2024, March 1(77): 832-841, DOI: https://doi.org/10.24412/1932-2321-2024-177-832-841