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-Vl?dicescu, 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".