Yu. M. Paramonov
BAYES-FIDUCIAL APPROUCH FOR AIRCRAFT SPECIFIED LIFE
NOMINATION
The problem of nomination of Retirement or Specified
Life (SL) of aircraft on the base of full-scale fatigue
test result processing is considered. SL can be defined
(1) by requirement of fatigue failure probability
limitation or (2) by economics reasons. For optimization
problem the Bayes-fiducial (BF) approach is offered. BF
decision is always a function of sufficient statistics
and, by contrast with maximum likelihood method, it is
based on the use of specific loss function. For the
problem of failure probability limitation in case when
sufficient statistics coincides with the sample itself
(for example, for Weibull distribution) usually the
Monte Carlo method is used but in this paper for the
distributions with location and scale parameters an
analytical solution is offered. Some numerical examples
for lognormal, Weibull distributions are given.
O.V.Abramov, Y.V.Katueva and D.A.Nazarov
CONSTRUCTION OF ACCEPTABILITY REGIONS FOR PARAMETRIC
RELIABILITY OPTIMIZATION
The problem of representation and analysis of analog
technical devices and systems acceptable regions is
introduced. This problem occurs during designing and
controlling in view of parametric dithering. The
algorithms of constructing circumscribed parallelepiped,
representation of acceptable region as a set of
non-overlapping parallelepipeds are offered. The
algorithm of acceptable region centre of mass
computation is offered as the example of utilizing the
acceptable region representation.
Farhadzadeh E.M., Muradaliyev A.Z., Farzaliyev Y.Z.
MATCHING OF CRITERIA THE DISCERNMENT OF THE FUNCTIONAL
CHARACTERISTICS
OF INDEXES OF RELIABILITY OF PLANTS EES
References on variation of reliability on the curves
received at analysis of statistical data can appear
erratic if not to consider a random in character of
assessments of indexes of reliability. The comparison
method of criteria of a discernment of the functional
characteristics indexes of reliability reduced at
ordinal and nominal dials of variation of argument.
Maxim Finkelstein
ON ENGINEERING RELIABILITY CONCEPTS AND BIOLOGICAL AGING
In this study, various stochastic approaches to
biological aging modeling are discussed. We assume that
an organism acquires a random resource at birth. Death
occurs when the accumulated damage (wear) exceeds this
initial value. Another source of death of an organism is
also taken into account, when it occurs as a consequence
of a shock or of a demand for energy, which is a
generalization of the Strehler-Mildvan's model.
Biological age, based on the observed degradation, is
also defined. Finally, aging properties of imperfectly
repaired systems are discussed. We show that aging slows
down with age in this case. This presents another
possible explanation for human mortality rate plateaus.
G. F. Kovalev
"SAFETY" AS A CHARACTERISTIC OF ONE OF THE SINGLE
RELIABILITY PROPERTIES
The paper deals with the problems of interrelation
between two most important properties of technical
(production) systems: safety and reliability that were
considered historically separately. However, recently
both properties have proven to be increasingly more
interrelated, which makes their joint study topical. And
the safety may be treated as the most important
reliability property, determining to a great extent all
the remaining single reliability properties. The
relation between the notions of "technical safety" and
"energy safety" is also studied.
B. A. Kulik
N-TUPLE ALGEBRA-BASED PROBABILISTIC LOGIC
The concept of "probabilistic logic" known in artificial
intelligence needs a more thorough substantiation. A new
approach to constructing probabilistic logic based on
the N-tuple algebra developed by the author is proposed.
A brief introduction is given to the N-tuple algebra and
its properties that provide efficient paralleling of
algorithms for solving problems of logical analysis of
systems in computer implementation are generalized.
Methods for solving direct and inverse problems of
probabilistic simulation of logical systems are
considered.
Nicholas A. NECHVAL, Konstantin N. NECHVAL
TECHNIQUE FOR FINDING SAMPLING DISTRIBUTIONS FOR TRUNCATED
LAWS
WITH SOME APPLICATIONS TO RELIABILITY ESTIMATION
In this paper, the problem of finding sampling
distributions for truncated laws is considered. This
problem concerns the very important area of information
processing in Industrial Engineering. It remains today
perhaps the most difficult and important of all the
problems of mathematical statistics that require
considerable efforts and great skill for investigation.
The technique discussed here is based on use of the
unbiasedness equivalence principle, the idea of which
belongs to the authors, and often provides a neat method
for finding sampling distributions. It avoids explicit
integration over the sample space and the attendant
Jacobian but at the expense of verifying completeness of
the recognized family of densities. Fortunately, general
results on completeness obviate the need for this
verification in many problems involving exponential
families. The proposed technique allows one to obtain
results for truncated laws via the results obtained for
non-truncated laws. It is much simpler than the known
techniques. The examples are given to illustrate that in
many situations this technique allows one to find the
results for truncated laws and to estimate system
reliability in a simple way.
G. Albeanu & H. Madsen, B. Burtschy, Fl. Popentiu-Vldicescu,
Manuela Ghica
BOOTSTRAPPING TIME SERIES WITH APPLICATION TO RISK
MANAGEMENT
The bootstrap method is an extensive computational
approach, based on Monte Carlo simulation, useful for
understanding random samples and time series. It is a
powerful tool, especially when only a small data set is
used to predict the behaviour of systems or processes.
This paper presents the results of an investigation on
using bootstrap resampling (different types: uniform,
importance based, block structured etc.) for time series
appearing during software life cycle (mainly the
software testing phase, and debugging), economics, and
environment (air pollution generated by cement plants)
in order to help the activity of staff working on risk
management for software projects, risk management in
finance, and those working on environment risk
management.
G.Sh. Tsitsiashvili
DISCRETE TIME MODELS OF FORWARD CONTRACTS INSURANCE
In this paper financial management model of forward
contracts insurance suggested in some works is
considered by means of risk theory and heavy tailed
technique. This model is based on a compensation
principle. It attracted large interest and called active
discussion among economists. So its mathematical
analysis is initiated as economists so mathematicians.
G.Sh. Tsitsiashvili
ANALYSIS OF PORTS RELIABILITIES
This paper is devoted to algorithms of a calculation of
ports reliabilities. A port is a no oriented graph with
fixed initial and final nodes. As accuracy so asymptotic
formulas are considered. Suggested algorithms have
minimal numbers of arithmetical operations.
Igor Ushakov, Sumantra Chakravarty
OBJECT ORIENTED COMMONALITIES IN UNIVERSAL GENERATING
FUNCTION FOR RELIABILITY AND IN C++
The main idea of Universal Generating Function is
exposed in reliability applications. Some
commonalities in this approach and the C++ language are
discussed.
Igor Ushakov
METHOD OF OPTIMAL SPARE ALLOCATION FOR MOBILE REPAIR STATION
Method of finding optimal spare stock for Mobile Repair
Station is suggested. Numerical calculations are
performed with use of real field data. It showed
significant improvement: probability of first fix for
suggested variant is 0.967 in comparison with 0.534 for
existing variant.
Andrey Kostogryzov
MATHEMATICAL MODELS AND SOFTWARE TOOLS FOR QUALITY
AND RISK MANAGEMENT ACCORDING STANDARD REQUIREMENTS
The offered mathematical models and supporting them
software tools complexes (M&STC) are purposed for a
systems analysts from customers, designers, developers,
users, experts of testing laboratories and certification
bodies, as well as a staff of quality maintenance for
any complex system etc. M&STC are focused on providing
system standard requirements on the base of modeling
random processes that exist for the life cycle of any
complex system. Models implement original author's
mathematical methodology based on probability theory,
theory for regenerating processes and methods for system
analysis. M&STC may be also used in training and
education for specializations "System engineering",
"Software engineering", "System safety and security",
"Information systems".
