RT&A
2016,
# 3(42) Vol.11
Gertsbakh I., Shpungin Y.
Reliability Of Heterogeneous (k,r)-out-of-(n,m) System
We consider a coherent binary system consisting of
components
of a-type and components
of b-type. The a-type and b-type components have i.i.d
lifetimes with cdf and
,
respectively. The a-type and b-type components are
stochastically independent. Our system is UP if at least a-type
components are up and at least components
of b-type are up.We present a simple formula for this system
lifetime cumulative distribution function.
Schäbe H., Shubinski I.
A Minimal Repair Model With Imperfect Fault Detection
In this paper we study a model of a
system with imperfect repair, where also detection of
failure might fail. For such a system we derive the lifetime
distribution function of the system and give bounds for the
mean life and the mean residual life function.
Farhadzadeh E.M., Muradaliyev A.Z.,
Ismailova S.M.
Quantitative Estimation Of The
Integrated Parameter
Of Safety Ability To Live Of Personnel EPS
Opportunity of a quantitative
estimation integrated parameters (IP) safety of ability to
live (AL) is one of the basic directions of decrease in a
traumatism and destruction of personnel EPS. In a basis of
the developed method and algorithm of calculation IP AL
there are differences of requirements of Rules AL observable
in practice from a level of their execution. Quantitative
estimations AL open new, earlier inaccessible opportunities
regarding the analysis and the control. For example, to
compare AL at enterprises EES, to reveal the directions
reducing AL, to estimate AL on various categories of
maintenance, tests and repair of the various equipment and
devices EES.
Karaseva E.
Ability of Logical and Probabilistic
Model
for Operational Risk Managemen
In this paper the application of
logical and probabilistic (LP) models for operational risk
estimation in bank is described, the method for economic
capital calculation to cover losses, caused by operational
risk, with top and bottom capital limits is offered. The
influence of repeated events on credit and operational risks
is demonstrated. Significances of such repeated events are
higher and actions to their minimization should be
top-priority.
Nechval N., Nechval K., Strelchonok V.
Constructing Tolerance Limits On Order
Statistics In Future Samples
Coming From Location-Scale Distributions
Although the concept of statistical
tolerance limits has been well recognized for long time,
surprisingly, it seems that their applications remain still
limited. Analytic formulas for the tolerance limits are
available in only simple cases. Thus it becomes necessary to
use new or innovative approaches which will allow one to
construct tolerance limits on future order statistics for
many populations. In this paper, a new approach to
constructing lower and upper tolerance limits on order
statistics in future samples is proposed. Attention is
restricted to location-scale distributions under parametric
uncertainty. The approach used here emphasizes pivotal
quantities relevant for obtaining tolerance factors and is
applicable whenever the statistical problem is invariant
under a group of transformations that acts transitively on
the parameter space. It does not require the construction of
any tables and is applicable whether the past data are
complete or Type II censored. The proposed approach requires
a quantile of the F distribution and is conceptually simple
and easy to use. For illustration, the normal and log-normal
distributions are considered. The discussion is restricted
to one-sided tolerance limits. A practical example is given.
Veretennikov A.
On Recurrence and Availability Factor
for Single–Server System
With General Arrivals
Recurrence and ergodic properties are established for a
single–server queueing system with variable intensities of
arrivals and service. Convergence to stationarity is also
interpreted in terms of reliability theory.
Fagge N., Ali U., Yusuf I.
Mean Time To System Failure Assessment
Of A Single Unit
System Requiring Two Types Of Supporting Device For
Operation
This paper studies the mean time to
system failure (MTSF) of single unit system operating with
the help of two types of external supporting device. Each
type of supporting device has two copies I and II. The
system is analyzed using differential difference equation to
develop the explicit expression for mean time to system
failure. Based on assumed numerical values given to system
parameters, graphical illustrations are given to highlight
important results.
Krishnamoorthy A., Sathian M.,
Viswanath N.
Reliability Of A
-out-of- System
With A Single Server
Extending Non-Preemptive Service To
External Customers.
Part I
We study repairable -out-of- system
with single server who provides service to external
customers also. N-policy is employed for the service of main
customers. Once started, the repair of failed components is
continued until all components become operational. When not
repairing main customers, the server attends external
customers (if there is any) who arrive according to a
Poisson process. Once selected, the external customers
receive a service of non-preemptive nature. When at least main
customers accumulate in the system and/or when the server is
busy with such customers, external customers are not allowed
to join the system. Otherwise, they join an infinite
capacity queue of external customers. Life time distribution
of components, service time distribution of main and
external customers are all assumed to follow independent
exponential distributions. Steady state analysis has been
carried out and several important system performance
measures based on the steady state distribution derived. A
numerical study comparing the current model with those in
which no external customers are provided service, is carried
out. This study suggests that rendering service to external
customers helps to utilize the server idle time profitably,
without affecting the system reliability.
Krishnamoorthy A., Sathian M.,
Viswanath N.
Reliability Of a
-out-of- System
With A Single Server
Extending Non-Preemptive Service To
External Customers.
Part II
In this paper we study a -out-of- system
with a single repair facility, which provides service to
external customers also. We assume an -policy
for service to failed components(main customers) of the -out-of- system
starts only on accumulation of of
them. Once started, the repair of external customers is
continued until all the components become operational. When
not repairing failed components, the server attends external
customers(if there is any) who arrive according to a Poisson
process. Once selected for service, the external customers
receive a service of non-preemptive nature. When there are
at least failed
components in the system and/or when the server is busy with
failed components, the external customers are not allowed to
join the system.Otherwise they join an orbit of infinite
capacity. Life time distribution of failed components,
service time distribution of main and external customers and
the inter retrial time distribution of orbital customers are
all assumed to follow independent exponential distributions.
Steady state analysis has been carried out and several
important system performance measures, based on the steady
state distribution, derived. A numerical study comparing the
current model with those in which no external customers are
considered has been carried out.This study suggests that
rendering service to external customers helps to utilize the
server idle time profitably, without sacrificing the system
reliability.
