Aim. Problems associated with the study of material fatigue, while being relevant in terms of engineering practice, have a significant degree of uncertainty. The fatigue curve is censored (which indicates the presence of items that have passed the planned load cycle and destroyed by the end of the tests), while the load block made for calculating durability can be designed in a number of ways with a sufficient share of subjective decisions. The load block is intended for calculating durability and defining test plans. It is to fully reflect the entire expected operational history. Both factors are considered in the paper as elements of fuzzy logic. The author examines the creation of a scientifically substantiated load block that would take into account the possible operating modes in a right proportion and taking into account the variability. That is due to the fact that fatigue damage accumulates over the entire life of a machine and is to be scientifically evaluated for an adequate probabilistic assessment.

Methods. As the modes of operation of a certain part are not precisely defined (and cannot be defined by virtue of the logic of random use of machines), projections of random fuzzy distributions are considered. A finite set of operating modes in a reasonable proportion was successfully scientifically substantiated. Using the example of load analysis of a critical part of rolling stock, distributions were constructed and the possible distribution of a part’s life was estimated. The output of the developed method will allow assessing the operational risks and predict the required number of spare parts. By taking into account the censored sample elements in the process of fatigue curve construction, the estimation of the fatigue curve parameters can be made more consistent.

Conclusions. The use of fuzzy sets may prove to be very useful when examining fatigue curves and estimating durability variation. Examples are given of applying the proposed method.

Aim. To suggest a method of estimating the parameters of a set of spare parts, tools and accessories (SPTA) according to data sheet specifications for industrial uninterruptible powers supplies (UPS) of data centres using state-of-the-art techniques.

Methods. The paper uses methods of the dependability theory, the Markov process theory and the optimisation method.

Results. Using the suggested approach, the stages of parametric synthesis of an SPTA kit were defined for mainline modular UPS that feature redundancy with repair and limited SPTA. For each stage, the application of mathematical models required for calculating the dependability characteristics and parameters of power module components based on UPS dependability indicators is substantiated along with the mathematical models that associate the sufficiency indicators of an SPTA kit with its parameters. Those models allow calculating the failure and recovery rates of UPS power modules, as well as the mean time to failure and restoration based on the data sheet specifications of reliability, maintainability and availability. In turn, the obtained dependability characteristics are the input data for calculating the SPTA sufficiency values (average delay in meeting a request). Using the value of average delay in meeting a request with an SPTA kit as a criterion for the mean time to power module restoration allows suggesting that it is, in principle, possible to ensure the specified dependability indicators in the course of its operation, and, therefore, such UPS can be used. Should the latter be possible, then using the value of average delay in meeting a request as a restriction, while taking into account the restrictions on the initial SPTA inventory, will allow synthesising the SPTA kit (select a replenishment strategy and define its parameters (delivery time, etc.). Comparing the logistical capabilities and the resulting data for the selected replenishment strategy will allow making a final conclusion regarding the capability to maintain the specified UPS dependability characteristics throughout the operation period. Using the above method, the parameters were synthesised of a single kit of spare parts, tools and accessories, using the Protect 3.M UPS as an example.

Conclusion. The approach suggested in the paper allows estimating both the general feasibility of ensuring the specified dependability, and the economic expediency of using industrial mainline modular UPS with redundancy and recovery. Additionally, if ensuring the UPS dependability is possible, but the operating costs of its maintenance are unacceptable, the possibility of reducing the number of repair teams (reducing the cost of their deployment) and/or using more efficient redundancy methods (mixed redundancy, mixed redundancy with rotation, etc.) should be evaluated. However, it should be taken into consideration that the proposed approach based on the use of mathematical models does not guarantee a 100% accuracy of SPTA parameter estimation, as the mathematical models that it uses, like any other models, have a limited accuracy and the results obtained with their help require experimental confirmation by means of testing or controlled operation.

Aim. The paper aims to develop an algorithm that would allow finding the required number of items (SPTA) for a complex system, whose elements may or may not be maintainable.

Methods. Markov models were used for describing the system. The final probabilities were obtained using the Kolmogorov equation. The Kolmogorov system of equations has a stationary solution. Classical methods of the probability theory and mathematical dependability theory were used.

Conclusions. The paper formalizes the problem of determining the required number of SPTAs for a system with elements that have a probability of being repaired. A Markov graph is constructed. Using induction, a stationary solution was found for the Kolmogorov system of equations. An example of finding the required number of SPTAs is given.

. Experts in applied dependability are showing an increasing interest in the Bayesian theory. However, the Bayesian approach is not generally accepted by mathematical statistics and dependability researchers. The doubts about its practical applicability are primarily due to the fact that it allows for subjective probabilities. In practice, homogeneous product models are normally considered, i.e., each item in the evaluated batch is characterized by the same selected dependability value. In the case of Bayesian statistical estimation, the model involves heterogeneous products, however, in the course of steady production, it is not considered normal to manufacture products with varied dependability, which calls into question the adequacy of Bayesian statistical estimation methods.

Aim. It is demonstrated that using Bayesian estimators that employ models designed for homogeneous products in dependability is erroneous.

Methods of research. For the purpose of finding effective estimates within a selected class, integral numerical characteristics of the accuracy of estimation were used, namely, total squared bias of the expected implementation of a certain variant estimate from the examined parameters of the distribution laws, etc.

Conclusions. 1. For any result, the realizations of Bayesian estimates are grouped within the dogma of mean – ≈p_α = 1 – α / (α + β), while classical ^≈Р₂ = 1 – R/N  and integral ^≈Р₄ unbiased estimates respond adequately to any external changes. The use of Bayesian estimates in dependability, when models designed for homogeneous products are employed, is erroneous, and there is no need to use them. 2. Bayesian estimates should only be used for groups of heterogeneous products. 3. Instead of Bayesian estimates, integral biased estimates should be used in dependability, when models designed for homogeneous products are employed.

Aim. To suggest a new method of energy-efficient traffic planning for subways. Traffic planning is understood as passenger train scheduling in compliance with all the applicable requirements and restrictions involving hourly performance in terms of the specified number of handled train pairs, efficient use of the theoretical and practical capacity of a given subway line, safety of vehicle traffic ensured by timely technical diagnostics of the rolling stock in the form of scheduled repairs and inspections in depots and/or lineside technical inspection stations, passenger comfort expressed in the uniformity of train delivery to stations, which, in turn, ensures the redistribution of passenger flows at stations and prevents congestion on platforms.

Methods. The paper uses methods of automated construction of target metro train schedules that are based on the criteria of train spacing uniformity, as well as uniformity of rolling stock distribution in the process of transition planning, with subsequent redistribution of delay times defined by the automation algorithm over the station-to-station travel times. The method of uniform travel times is based on minimizing the sum of square deviations of departure times for all stations and all trains. The method of vehicle uniformity within transition processes is based on the application of the Euclidean integer division algorithm. When preparing the paper, the authors took into account the fact that metro lines feature systems of various levels of automation regulated by the IEC 62290-1-2014 international standard. Attention was paid not only to transportation systems with high degrees of automation (classified as GoA3 and GoA4 in the standards), but those with low automation (classified as GoA0, GoA1 and GoA2) as well.

Results. The method proposed in the paper clearly shows reduced power consumption associated with train traction that is proportional to the durations of delayed departures defined by the automation algorithms of the intelligent automated system for target metro train schedule construction.

Conclusions. The presented approach clearly indicates a direct correlation between the energy efficiency of a train schedule and the uniformity of distribution of control actions that adjust train spacing and the durations of the adopted delays, defines the sequences of added/removed units of rolling stock within transition processes, as well as rational night-time train allocation. The materials presented in the paper extend the available knowledge in the field of automation of metro train traffic planning, thus enabling further improvement of the methods of intelligent transportation system design that take into account the deployed highly automated train driving systems (GoA3 and GoA4).

The paper Aims to reduce the cost of onboard train control systems by using an architecture with a single-channel source of information (in this case, axle counters) and a two-channel receiver of information (in this case, an on-board control system) instead of the conventional architecture, whereas the generator and receiver are to have at least two channels. Additionally, in order to ensure the system’s safety, the failure detection mechanism embedded in the most common multichannel architecture that involves comparing the outputs of the onboard unit’s channels is complemented by software verification algorithms that enable a SIL4-compliant level of correct failure detection of the single-channel device (in this case, an axle counter). This level is primarily characterized by the quantitative indicator “probability of correct detection” and achieving the goal requires calculating the acceptable and, at the same time, achievable range of this probability and the performance parameters of the verification algorithms, of which it is a function.

Methods. The paper shows two safety models of an onboard train control system, i.e., the conventional architecture with two-channel generating and receiving devices and the architecture with a single-channel source and a two-channel receiver of information. The graph models feature similar states and only differ in terms of the model parameters. By applying the topological method [1] to the conditions of the problem, within both models, formulas were derived for calculating the mean time to hazardous failure, rate and probability of hazardous failures. Input values were identified, including the probabilities of correct detection of failure of the on-board system and axle counter, the values of those safety indicators were calculated, allowing to attribute the system to one of the four discrete safety integrity levels.

Results. The paper defines the probabilistic performance indicators of failure detection software and hardware for an architecture with a single-channel source and a two-channel receiver of information. Indicator definition involves setting maximum permissible values that enable the quantitative safety indicators (mean time to hazardous failure, rate and probability of hazardous failures) not worse than those of a conventional architecture with twochannel generating and receiving devices. The efficiency parameters that are the most safetycritical due to their significant effect on correct failure detection (in this case, the axle counter) are identified. The findings show that it is possible to reduce hardware-related costs without compromising compliance with the safety requirements when using single-channel sources (in this case, axis counters) and two-channel receivers of information (in this case, an on-board control system) that feature software enabling an appropriately high level of correct failure detection (in this case, of an axle counter).

Today, when operation of commercial plants is organised, they are expected to comply to constantly increasing requirements for safety, dependability and efficiency of operation. The methods and procedures that are employed for the purpose of improving the safety and dependability of commercial plants are based on the information on the dependability of components, systems and equipment. In order to identify the objective dependability characteristics of such facilities, their behaviour in operation is monitored. In the course of facility operation monitoring, periods of continuous fault-free operation, periods of downtime, causes of downtime, failures, defects and malfunctions of items, frequency and depth of preventive maintenance of elements and systems, as well as other information are recorded. It should be noted that elements and systems of today’s industrial facilities, such as nuclear power plants, petrochemical complexes, etc., are classified as highly dependable equipment. Failures of such equipment are rare. The number of same-type facilities is extremely small.

Aim. Given the above, the problem arises of developing methods for reliable estimation if item dependability characteristics on the basis of limited statistical information.

Method. The paper examines a method for calculating facility dependability indicators on the basis of statistical information obtained in operation, i.e. a method for minimising the risk function while taking into account left-truncated and right-censored data for the purpose of Weibull distribution parameter estimation.

Conclusions. By way of example, the authors refer to a method for evaluating dependability indicators based on complete, right-censored and left-truncated operation times, as, in practice, such combination is quite common. The form of likelihood functions for the Weibull distribution is given. A test case is examined, whereas, using the risk function minimisation, estimates of the Weibull distribution parameters are obtained for a sample that contains full, left-truncated and right-censored data. The authors examined the variation in the Weibull distribution values and their accuracy depending on the proportion of truncated and censored data.

Aim. The paper examines matters related to the definition of the architecture and requirements for data communication networks as part of intelligent mass transit management systems.

Methods. The paper suggests a network architecture using multiprotocol label switching (MPLS) technology and traffic routing. If the core of a local area network is implemented using fully-connected topology, the use of flow labels allows predefining information exchange routes between servers and applications of an information and telecommunications network (ITS). Multiprotocol label switching (MPLS) is the foundation of control and information acquisition networks of ITS. That allows adopting common interfaces to the subsystems that perform various functions within an ITS, e.g., control and diagnostics, minimizing the time of information delivery to management servers and sending critical control commands, as well as using common Ethernet or 4G/5G wireless interfaces.

Conclusions. The path installation/removal principle, when applied to critical facilities, significantly complicates attacks and collection of information on the network structure of ITS.