Abstract. Aim. The paper aims to examine the application of a multinomial distribution as part of valuation of the number of an object’s failures. It is assumed that the valuation is “based on past experience” (a statistical sample of the number of an object’s failures accumulated over several preceding evaluation periods).

Methods. The paper uses methods of system analysis, probability theory and mathematical statistics. The author analyses the primary indicators used to define the applied dependability indicators. It is noted that the valuation of such indicators based on statistical data for complex systems appears to be promising. The problem of valuation of the number of failures using a statistical sample is examined. The primary disadvantages of the used approaches are identified that are associated with errors in defining the average values of series, variation coefficients and asymmetry. It is shown that it is possible to solve the problem using the well-known combinatorics problem “on balls and boxes”, which leads to the use of a multinomial distribution. The paper examined the definition of probabilities for compositions and partitions of the number n into m parts, as well as the probabilities of a given number of balls being in a box with their maximum number. The author also considered formulas and algorithms that allow reducing the number of calculations in case of machine computation of the probabilities of a multinomial distribution. The feasibility of approximating a discrete distribution function by the Gumbel distribution is estimated. The paper demonstrates the feasibility of valuating the number of failures for a “segment” corresponding to a part (fraction) of an object’s dimension considered on a certain part (fraction) of the time interval. It also examines examples of valuating the number of failures for an object as a whole over a 1-month evaluation interval and for ½ of an object over a 12-month evaluation interval, while the total interval for which the statistical sample is accumulated is 72 months. The paper sets forth limitations on the application of the presented method and notes some of its possible advantages. In particular, it is noted that the statistical sample is only one implementation of the multinomial distribution, so it can be said that when applying the proposed method, the results of valuation are no longer affected by the presence of unlikely combinations of series values in the statistical sample. It is also noted that when applying the proposed method of valuating the number of failures, the obtained acceptable value will never be less than or equal to the average value of the statistical sample.

Results. Formulas have been obtained for calculating, based on partitions, of the discrete density number and the maximum distribution function of a multinomial distribution. The paper presents the results of algorithm analysis for machine computation. The results of applying some algorithms are presented. A formula is proposed for approximating the distribution function of the maximum of a multinomial distribution using the Gumbel distribution (for the largest values) using the method of moments. The author recommends a range of values of the estimated interval, in which the proposed method provides acceptable reliability of the results. The task of further research is defined.

Abstract. Aim. Systematic failures, unlike random hardware failures, cannot be described using the mathematics of the probability theory and the dependability theory. However, such failures are the biggest problem due to their unpredictability. In the case of describing systematic failures of unique highly vital systems, a solution is presented by an approach that involves taking into account the quantitative criteria of functional performance of a facility in time that are defined, for example, by prescribing a set of parameters for each function that characterize its ability to perform, as well as acceptable limits for such parameters’ variation. The paper aims to develop an approach to the use of expert evaluation for the purpose of identifying the type and parameters of the distribution of the time to failure of unique highly vital elements. The author examined an approach to determining the a priori distribution of the time to failure of unique highly vital elements by pairwise comparison that would be useful for improving the accuracy of their dependability indicators.

Methods. Hierarchy analysis, fuzzy logic and permutation theory were used. Fuzzy variables were introduced, the degrees of belonging to which are interpreted as subjective probabilities of the time to failure and its characteristics within different time intervals. Methods were proposed for accounting for the accuracy of expert evaluation and for solving the cluster sampling problem.

Abstract. Aim. To identify one of the problems of professional psychological selection of applicants for training in a higher military flight school, to show the importance of moral values in the professional development of a military pilot and the impact of their presence or absence on the quality of the prediction as part of professional psychological selection. At present, the progress and constant modernisation of the Russian Air Force aircraft fleet places ever higher demands on the level of professionalism of a modern military pilot. In this context, there is a growing need for greater numbers of indicators diagnosed during professional psychological selection (PPS) that are later used to predict the success of military flight training and professional activity in general. That is primarily due to the fact that recently more and more attention has been paid to the role of the personality and its integrative function. However, at present, the existing flight crew PPS system does not provide a comprehensive diagnosis of a candidate’s personality.

Methods. Based on a theoretical analysis of the work conducted by researchers and practitioners of aviation psychology and various approaches to the study of the professional fitness of flight personnel, it was identified that the key element in the diagnosis of professional fitness is the personality with its integrative function and the whole set of professionally important qualities. The analysis of literature in aviation psychology shows that personal qualities determine motivation, focus and sustained interest in flight work, as well as the social type of behaviour and a person’s adaptation to specific conditions of flight activity and military service.

Results. A pilot’s professionalism begins with shaping the personality. Nowadays, the loss of spiritual guidelines has led to a dramatic simplification of moral values and patriotic spirit, and young people are more focused on consumerism. Selecting candidates for military aviation involves the use of a diverse set of diagnostic techniques that helps evaluate the most important psychological and personal qualities. However, the experience of application of personal questionnaires shows that they do not always represent a complete picture of an applicant’s motivation, personality orientation, self-awareness and basic values. The use of projective and hardware-based methods is minimised, the existing automated system for professional psychological selection (ASPPS) is insufficiently equipped with methods that diagnose personal qualities, the emphasis being placed on diagnosing cognitive processes. The century-old history of PPS shows a violation of the principle of personal integrity, which is

expressed in the bias towards psychophysiology. As a result, at present, the existing flight crew PPS does not provide a comprehensive diagnosis of a candidate’s personality.

Conclusions. In conclusion, it is noted that the key element in the diagnosis of professional aptitude is the  personality with all its PIQ and moral values. Growing numbers of diagnosed indicators in the personal block of the PIQ will enable a comprehensive diagnosis of a candidate, and thanks to a combination of survey and projective methods, it will help increase the reliability of the PPS prediction, provided that an applicant’s personality is treated holistically, based on the principles of an integrative approach to the person as an integral personality.

Abstract. Aim. The paper aims to evaluate the indicators of safety and reliability of the MALS suite of technology that ensures the control of locomotives. Increased indicators are achieved through the use of additional controls. As such, a second virtual channel is proposed. The latter allows detecting MALS failures without affecting the shunting engine control algorithms.

Methods. The paper uses the graph method. Using a modified topological semi-Markov method, formulas were deduced for calculating the mean time to failure and the safety factor.

Results. The paper individually examines the mean time of the automatic train operation system of a shunting engine remaining in at least SIL3 and mean time to hazardous failure. The authors research the dependence of the above indicators on the failure rate of the MALS equipment and the machine vision. Using the graph method, the level of the system’s functional safety was evaluated by calculating the safety factor and the danger factor. The dependence of the above factors on the system recovery time and probability of detection of component failures was examined.

Abstract. Railway signalling automation devices have been around for quite some time. Many systems in operation are considered obsolete. At the same time, modernization does not cover the whole Russian railway system. The deployment of monitoring systems since the beginning of the 2000s made the maintenance of bulky signalling systems more comfortable, reduced the time of fault detection. The second decade of the 21-st century saw a widespread deployment of information technologies in various spheres of life, including industry, yet at a slower pace, especially in railway transportation. One of the innovations was the emergence of the artificial intelligence, which enabled more progressive maintenance of devices through prediction of pre-failure states. The latter allows notification of technical personnel by an intelligent system that processes significant parameters of the observed facility or process, thereby replacing manual monitoring that requires time and professional experience.

Aim. To suggest the use of artificial intelligence-based methods in railway signalling devices based on the existing technical diagnostics and monitoring systems. Methods. Python-based unsupervised machine  learning methods are used to create, process and visualise data.

Results. The AI models showed a reaction to anomalous changes in the temporal characteristics of code generators.

Conclusion. An AI-enabled program can serve as the core for processing data related to the monitoring of railway signalling devices and requires careful research in predicting their known failures at the signal point.

Abstract. Aim. The aim of the paper is to construct a non-simulation method for finding the confidence interval for the probability of an upper-level event of a failure tree. Iterative Monte Carlo algorithms require very much time and computational resources, especially for large fault trees. Therefore, developing “fast” algorithms for finding uncertainty in a calculated fault tree is extremely important.

Methods. The algorithm was developed using classical methods of the probability theory, mathematical statistics and dependability theory. The mathematical foundation of the algorithm is the central limit theorem and certain properties of the dispersion of a random variable from the probability theory. To simplify calculations, the confidence interval was built on the assumption of a lognormal distribution of the failure rate estimate with a certain specified error factor. The initial information consists of a set of minimal cross-sections defined for the fault tree using specialized software tools, as well as dependability parameters of the events in each of the cross-sections. The cross-sections may contain dependent events that are part of common cause failure (ССF) groups. Various ССF accounting models, including the betafactor model, alpha-factor model, etc., can be used to calculate the probability of such events. To simplify the set of cross-sections, a program code is used that groups the cross-sections that are identical in value and meaning.

 Results. A conservative method for constructing a confidence interval for the probability of an upper-level event in a fault tree was developed. The method is not iterative and allows identifying the uncertainty of the final result for randomly-sized fault trees.

Conclusions. The algorithm for identifying the uncertainty can be used instead of the Monte Carlo method in specialized software suites that calculate fault trees.

Abstract. Aim. The author has developed a criterion to test the hypothesis of a uniform distribution for random variable observations in small samples. The criterion is built by using sample observations to construct a variation series in ascending order and dividing each previous term of this series by the extreme term, then discarding it. The resulting new variation series is processed similarly until there is only one quotient left that is the criterion value.

Methods. The paper uses methods of the probability theory and mathematical statistics.

Results. The suggested criterion is sufficiently efficient for distinguishing between samples of minimal size for statistically similar hypotheses, such as the hypothesis of a uniform distribution law and the hypothesis of a beta distribution of the first kind.

Conclusions. The approach suggested in the paper makes it quite simple to implement the sequential analysisprocedure (detection of a “dissonance” in a process). Such a procedure allows detecting a “dissonance” (deviation of the distribution of observations from the uniform law) with a practically sufficient rate.

Abstract. Aim. The paper examines the methodological aspects of estimating the optimal reserve capacity in a concentrated electric power system. The sources of errors in the Markovich formula are identified. It is shown that the key requirement for the applicability of the Markovich formula is the assumption of absolute dependability of additional backup power units. The author analysed the mathematical procedures for identifying the probability and mathematical expectation (ME) of power shortage (PS). He proposed formulas that allow analytically identifying the MO and the PS variance. It is proposed to represent the schedule of scheduled repairs of main generation equipment as a deterministic component of the additional load, which allows abandoning the random processes model in favour of random variables. It is shown that there is an almost linear functional relationship between the probability and the ME of PS, which allows estimating the adequacy indicators based on the interval probability of the PS.