The paper presents a calculation method for detecting and eliminating outlying values. It is shown that its effectiveness depends on the amount of a priori information on the examined process. The proposed method is used for cases whereas the process is stationary and has a Gaussian probability density law. When analysing non-stationary random processes, the existing methods and algorithms rely on the fact that the outlying component is additive and the characteristics of the outlying values are known a priori. The work used the statistical decisions theory that allows formalising the verification algorithms and selecting a criterion for detecting outlying values. Both parametric and non-parametric methods were proposed. In the first case, it is required to have a priori information both on the function of the useful component and on the distribution law of the outlying component of the process, as well as its parameters. It is postulated that the use of non-parametric processing methods requires significantly less a priori information, but their effectiveness is defined by the processing parameters that, in turn, depend on the function of the useful and the distribution law of the outlying components of the process. It is noted that an outlier may prove to be one of the extreme values of the probability distribution of a random variable. The authors outline the problems of ambiguity of input data in case of classical computing. The paper examines the way the external factors affect the dependability and the degree to which such factors are taken into consideration in the existing methods. Methods for assessing the life of the examined items are presented, among which control chart-based methods hold a prominent place. It is shown that the range proves to be a more convenient measure for data dispersion calculation than the standard deviation. Plotting the range of sample on a control chart along with the expectation makes it easier to notice an anomaly. The range is a rough measure of the rate of change of the monitored variable and its value may exceed the control limits on the range chart and inform of an anomaly much earlier than the change in the mean that may still be within the specified control limits.

Abstract. Aim. To propose a methodological approach to probabilistic forecasting and comparison of the performance of systems producing material and/or information products, to illustrate the practicality of the proposed approach with examples in various applications. Methods. Methods and models based on the methods of probability theory and system analysis, brought to implementation in national standards of system engineering, are proposed for use. Results. Models of complex systems producing material and/or information products are adapted for predicting and comparing for the same system under different operating conditions, for different systems applied to the same time period or for different time periods with the same or different duration and operating conditions. The proposed approach covers methods for assessing the relative part of the system functions performed with acceptable quality, estimating costs in the life cycle of systems, assessing the relative degree of satisfaction of stakeholders associated with quality and costs in system operation. Conclusions. The efficiency of the proposed methodological approach to probabilistic forecasting and comparison of the performance of systems of various applications under conditions of uncertainty is demonstrated. The approach can be used for system analysis and optimisation of the performance of systems producing material and/or information products, substantiation of quantitative system requirements and engineering solutions aimed at meeting the needs of stakeholders.

Point estimation is one of the most common forms of statistical inference. This paper touches upon the concepts of unbiasedness and effectiveness of biased estimates. An attractive approximation for the true (quantitative) value of the estimated parameter t whose values belong to a certain numerical set t T is an estimate , for which the sum of the mathematical expectation of the square of the differences between the possible realization of and the estimated parameter t is minimal (least squares estimation). Another approach is to find the value of the parameter t based on the sum of the mathematical expectation of the difference between the possible realisation ϵ = xi and the estimated parameter t, provided that this sum is zero, so that the positive and negative differences are balanced ∑(xi – t) = 0. Implementations of N independent random values have a general distribution that depends on the estimated parameter t. There are other approaches, but at present there is no single convincing definition of the optimality of finding effective estimates. The well-known statistician Box wrote: “All models are wrong, some are useful.” It is not always easy to establish the adequacy of a model, so our choice is defined by its utility! The simple effectiveness criterion of biased estimates given below is too convenient, however this does not mean that the assumption of the effectiveness of biased estimates based on this criterion is true, yet the usefulness of this simple and convenient model is obvious. The Aim of the paper. The paper aims to construct a simple effectiveness criterion of biased estimates and obtain simple effective estimates of dependability indicators for a binomial test plan and a test plan with limited time and recovery using the constructed simple effectiveness criterion of biased estimates. Conclusions. A simple effectiveness criterion of biased estimates was obtained that compensates for the effect of unequal dispersion values and the square of the bias. New effective biased estimates of various dependability indicators were obtained for a binomial test plan and a plan with limited test time and recovery of failed items.

Aim. To identify and classify the technical limitations of the Markov method of system dependability analysis, to define their boundaries taking into account the actual feasibility of the method, to show the opportunities of expanding the applicability of the Markov method. The paper examined the limitations associated with the automation of state graph construction and the mathematical solution of the corresponding systems of algebraic and differential equations using software. Methods. An approach is proposed to automatically constructing state graphs of technical systems defined by a structural diagram of dependability, as well as communication networks defined by a structural diagram. The paper examines approaches to reducing the dimension of a state graph that do not reduce the accuracy of dependability indicator calculation. The author also considers ways of reducing the dimensionality of a state graph by means of truncation or merging inoperative states that cause biased calculated dependability values. Results. The actual limits of applicability of the Markov method are shown along with their relevance in the context of modern information technologies. Approaches are shown that expand the applicability of the Markov method for analysing the dependability of large systems. The existing approach to state graph truncation were examined. Approaches to merging inoperative graph states were proposed and investigated (for bias). Conclusion. The approaches discussed in the paper allow extending the applicability of the Markov method of system dependability analysis to systems with a larger number of subsystems.

Aim. The paper aims to create and verify methods for predicting the dependability of autonomous power supply to local low-power consumers. Methods. The work uses simulation tools, i.e., computational experiment for predicting the dependability and safe service life of autonomous cluster distributed energy networks that include various power generation installations, power transmission lines and an automated self-regulation system for the purpose of diversifying the risks of failure. Results. Using methods of probabilistic analysis of technical system safety, the dependability of power supply is predicted in terms of possible energy network failures and threats to the life of consumers. The problem can be solved by simulating and predicting the moment of failure of a power network, i.e., critical violation of design conditions, accident, etc. This scenario allows – for long periods of operation – simulating failure situations due to degradation and destruction of elements, units, power lines, as well as failures under multidimensional uncertainty of prediction of dependability and quality of power supply. The key output of simulation is a set of recommendations to ensure energy security. The paper presents simulated dependability indicators, analysis of the effect of structural design solutions underlying a distributed energy network on the dependability and energy security. Conclusion. The use of computational experiments and results of power supply dependability simulation as part of predicting probabilistic indicators of failures of equipment and elements of cluster energy networks, identifying their consequences for the energy security of sparsely populated and remote locations lays the foundation for quality management of energy networks. Additionally, in the future, additional causes and initial events may be included in the model for the purpose of studying the facts of failures. For instance, such causes as uneven generation using renewable sources, finite fuel supply for conventional generation sources, reliability of the power grid personnel. The proposed approach allows verifying promising new energy network design solutions, for example, including energy storage systems into a distributed energy network that – at various points in time – may be either “generators” or “consumers”. Simulation of local energy networks is of practical interest and is important for improving their consumer quality, resistance to hazardous environmental effects.

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

Aim. The paper aims to compare the results of vibration diagnostics at different wheel pair (WP) rotation speeds based on the peak signal values and noise from the front bearing of the WP axle box equipped with a SOP AK 32.01 cylindrical roller with a standard defect. Methods. The peak vibration signal values were analysed using WP with different wheel tread thicknesses, i.e., 25, 45, and 65 mm. The bearing of one of the axle boxes (front) was equipped which a defective SOP AK 32.01 roller. Results. In the course of the experiment, it was found that as the thickness of the wheel tread grows the probability of over-rejection increases, which is practically confirmed by the fitness of the parts and components of the axle box upon dismantling and careful inspection. Conclusion. The “Reject” conclusion issued by the UDP-2001SM vibration stand should directly depend on the WP rotation speed. Additionally, its rotation rate should be selected depending on the thickness of the wheel tread.

Aim. The paper is dedicated to describing the validation of risk analysis as part of an automated train control research project. Methods. Validation was performed using several different methods. The obtained results were compared with those obtained from other sources. Additionally, an independent risk analysis was performed using the alternative MEM (minimum endogenous mortality) method. Results. The validation showed that the project’s findings are reliable. Safety Integrity Levels (SIL) 1 or 2 were confirmed for train driver substitution systems. Conclusions. It was shown that various methods should be used for the purpose of risk analysis validation. It must be taken into account that comparable, but not identical results will be obtained.