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30 pages, 3404 KiB

Open AccessArticle

Calculation of the System Unavailability Measures of Component Importance Using the D²T² Methodology of Fault Tree Analysis

by John Andrews and Sally Lunt

Mathematics 2024, 12(2), 292; https://doi.org/10.3390/math12020292 - 16 Jan 2024

Viewed by 630

Abstract

A recent development in Fault Tree Analysis (FTA), known as Dynamic and Dependent Tree Theory (D²T²), accounts for dependencies between the basic events, making FTA more powerful. The method uses an integrated combination of Binary Decision Diagrams (BDDs), Stochastic [...] Read more.

A recent development in Fault Tree Analysis (FTA), known as Dynamic and Dependent Tree Theory (D²T²), accounts for dependencies between the basic events, making FTA more powerful. The method uses an integrated combination of Binary Decision Diagrams (BDDs), Stochastic Petri Nets (SPN) and Markov models. Current algorithms enable the prediction of the system failure probability and failure frequency. This paper proposes methods which extend the current capability of the D²T² framework to calculate component importance measures. Birnbaum’s measure of importance, the Criticality measure of importance, the Risk Achievement Worth (RAW) measure of importance and the Risk Reduction Worth (RRW) measure of importance are considered. This adds a vital ability to the framework, enabling the influence that components have on system failure to be determined and the most effective means of improving system performance to be identified. The algorithms for calculating each measure of importance are described and demonstrated using a pressure vessel cooling system. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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21 pages, 363 KiB

Open AccessArticle

Stochastic Orderings of the Idle Time of Inactive Standby Systems

by Mansour Shrahili and Mohamed Kayid

Mathematics 2023, 11(20), 4303; https://doi.org/10.3390/math11204303 - 16 Oct 2023

Viewed by 567

Abstract

In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime [...] Read more.

In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime distributions, then the idle time of a failed cold standby system is smaller than the sum of the idle times of the components in the system according to the likelihood ratio order. In order to compare the idle time of two cold standby systems with different numbers of spares and different observation times of the failure in terms of the likelihood ratio order, an additional result is presented. Finally, we establish sufficient conditions for the usual stochastic ordering between the idle time of a cold standby system of size two and the sum of the idle times of the components in the system. We provide several examples to show that the results are achievable. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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25 pages, 4338 KiB

Open AccessArticle

Mathematical Analysis of the Reliability of Modern Trolleybuses and Electric Buses

by Boris V. Malozyomov, Nikita V. Martyushev, Vladimir Yu. Konyukhov, Tatiana A. Oparina, Nikolay A. Zagorodnii, Egor A. Efremenkov and Mengxu Qi

Mathematics 2023, 11(15), 3260; https://doi.org/10.3390/math11153260 - 25 Jul 2023

Cited by 10 | Viewed by 710

Abstract

The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. [...] Read more.

The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. Under the influence of external factors and specific operating modes, the technical condition of the equipment is continuously deteriorating, reliability indicators are decreasing, and the number of failures is increasing. Using the mathematical theory of reliability, probability theory and mathematical statistics, numerical methods of solving nonlinear and transcendental equations, this article defines the conditions of diagnostics depending on the intensity of failures and the given probability of failure-free operation of the equipment. Additionally, the inverse problem of determining the current reliability of electrical engineering systems depends on the terms of diagnostics and the intensity of failures being solved. As a result of the processing of statistical information on failures it is established that for the electrical equipment of a trolleybus, after a number of repair measures, the maximum density of failures occurs at a lower mileage, and the probability of failure-free operation can vary depending on the degree of wear of the equipment, i.e., on the number of previous failures. It is theoretically substantiated and experimentally confirmed that the reliability of trolleybus electrical equipment changes according to the exponential law of distribution of a random variable. It has been established that the real averaged diagnostic terms regulated by instructions are not optimal in most cases and differ several times from those defined in this paper. The dependence of switching equipment run-in on time has been clarified, which served as a prerequisite for specifying the inter-repair period for various types of trolleybus electrical equipment. A method of adjustment of the inter-repair time for the electrical equipment of trolleybuses is proposed. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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17 pages, 333 KiB

Open AccessArticle

Stochastic Comparisons of Lifetimes of Used Standby Systems

by Mohamed Kayid and Mashael A. Alshehri

Mathematics 2023, 11(14), 3042; https://doi.org/10.3390/math11143042 - 09 Jul 2023

Cited by 1 | Viewed by 613

Abstract

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold [...] Read more.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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13 pages, 1189 KiB

Open AccessFeature PaperArticle

Combined m-Consecutive-k-Out-of-n: F and Consecutive k_c-Out-of-n: F Structures with Cold Standby Redundancy

by Ioannis S. Triantafyllou

Mathematics 2023, 11(12), 2597; https://doi.org/10.3390/math11122597 - 06 Jun 2023

Cited by 1 | Viewed by 689

Abstract

In the present work, we study the combined m-consecutive-k-out-of-n: F and k_c-out-of-n: F reliability systems, which consist of independent and identically distributed components. Two different redundancy policies are considered, and their general frameworks are [...] Read more.

In the present work, we study the combined m-consecutive-k-out-of-n: F and k_c-out-of-n: F reliability systems, which consist of independent and identically distributed components. Two different redundancy policies are considered, and their general frameworks are described and illustrated. The main objective of the paper refers to the investigation of the effect of adding cold standby redundancy to the system at the the system level and the component level. Exact formulae for determining the crucial characteristics of the enhanced structure, such as its survival function, the mean time to failure and the mean residual lifetime, are provided. All formulae proved in the present manuscript are explicit expressions which are based on the signature vector of the resulting reliability schemes. An extensive numerical investigation is carried out to shed light on the performance of the combined m-consecutive-k-out-of-n: F and consecutive k_c-out-of-n: F reliability systems with cold standby redundancy. Some concluding remarks and comments are provided upon the determination of the optimal design parameters. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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18 pages, 2546 KiB

Open AccessArticle

Discrete Model for a Multi-Objective Maintenance Optimization Problem of Safety Systems

by Radim Briš and Nuong Thi Thuy Tran

Mathematics 2023, 11(2), 320; https://doi.org/10.3390/math11020320 - 07 Jan 2023

Viewed by 1094

Abstract

The aim of this article was to solve a multi-objective maintenance optimization problem by minimizing both unavailability and cost through the use of an optimal maintenance strategy. The problem took into account three different system designs upon which the objective functions are dependent, [...] Read more.

The aim of this article was to solve a multi-objective maintenance optimization problem by minimizing both unavailability and cost through the use of an optimal maintenance strategy. The problem took into account three different system designs upon which the objective functions are dependent, and the time to start preventive maintenance (PM) was used as a decision variable. This variable was optimized for all system components using a discrete maintenance model that allows for the specification of several discrete values of the decision variable in advance to find the optimal one. The optimization problem was solved using innovative computing methodology and newly updated software in MATLAB, which was used to quantify the unavailability of a complex system represented through a directed acyclic graph. A cost model was also developed to compute the cost of different maintenance configurations, and the optimal configuration was found. The results for a selected real system (a real fluid injection system adopted from references) showed that unavailability was less sensitive to variations in maintenance configurations, while cost variations were more noticeable in relation to different maintenance configurations. Applying PM, the increasing value of the decision variable increased cost because it led to more frequent corrective maintenance (CM) actions, and recovery times due to CM were more expensive than recovery times due to PM. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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20 pages, 3622 KiB

Open AccessArticle

Recovery Analysis and Maintenance Priority of Metro Networks Based on Importance Measure

by Hongyan Dui, Yuheng Yang, Yun-an Zhang and Yawen Zhu

Mathematics 2022, 10(21), 3989; https://doi.org/10.3390/math10213989 - 27 Oct 2022

Cited by 3 | Viewed by 1156

Abstract

The metro network plays a vital role in the urban transportation system. However, the metro network is easily damaged by humans and natural disturbances. This can cause serious economic damage, such as the suspension of metro station operations and line disruptions. Therefore, we [...] Read more.

The metro network plays a vital role in the urban transportation system. However, the metro network is easily damaged by humans and natural disturbances. This can cause serious economic damage, such as the suspension of metro station operations and line disruptions. Therefore, we conducted this study in order to minimize the loss caused by the damage to the metro network and improve the performance of the network after recovery. Based on the cascading failures of metro networks, this paper proposes a recovery model for metro networks considering the value of time. Then, considering the time value, a new node importance measure is proposed using the determination of maintenance priorities. The maintenance priorities of nodes with different importance values are investigated to minimize network losses. Lastly, the applicability of the method is verified by a metro network in Zhengzhou city. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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Review

Jump to: Research

31 pages, 3553 KiB

Open AccessReview

Review Models and Methods for Determining and Predicting the Reliability of Technical Systems and Transport

by Nikita V. Martyushev, Boris V. Malozyomov, Svetlana N. Sorokova, Egor A. Efremenkov, Denis V. Valuev and Mengxu Qi

Mathematics 2023, 11(15), 3317; https://doi.org/10.3390/math11153317 - 28 Jul 2023

Cited by 22 | Viewed by 2018

Abstract

Modern power and transportation systems are subject to high requirements for reliability and performance in performing their specified functions. At the same time, these requirements are constantly increasing with the increasing complexity of technology and the introduction of electronics and computer technology into [...] Read more.

Modern power and transportation systems are subject to high requirements for reliability and performance in performing their specified functions. At the same time, these requirements are constantly increasing with the increasing complexity of technology and the introduction of electronics and computer technology into its structure. This is fully applicable to energy and transportation infrastructure, including electric vehicles. The complexity of the systems and increasing requirements for them have led to the fact that the problem of increasing their operational reliability has acquired great importance. The article presents a review of methods and justification of ensuring a high level of reliability and serviceability of technical systems as one of the most important tasks in the creation and operation of complex systems, such as modern energy and transportation systems. It is shown that a significant reserve in solving the problem of increasing the reliability and performance of technical systems is the information on failures and malfunctions of these systems obtained from the field of operation. The methodology of collection and processing of statistical information on failures of vehicles described by different distribution laws is outlined. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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26 pages, 7600 KiB

Open AccessReview

Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis

by Elena Zaitseva, Vitaly Levashenko, Ravil Mukhamediev, Nicolae Brinzei, Andriy Kovalenko and Adilkhan Symagulov

Mathematics 2023, 11(11), 2551; https://doi.org/10.3390/math11112551 - 01 Jun 2023

Cited by 5 | Viewed by 2076

Abstract

Drones, or UAVs, are developed very intensively. There are many effective applications of drones for problems of monitoring, searching, detection, communication, delivery, and transportation of cargo in various sectors of the economy. The reliability of drones in the resolution of these problems should [...] Read more.

Drones, or UAVs, are developed very intensively. There are many effective applications of drones for problems of monitoring, searching, detection, communication, delivery, and transportation of cargo in various sectors of the economy. The reliability of drones in the resolution of these problems should play a principal role. Therefore, studies encompassing reliability analysis of drones and swarms (fleets) of drones are important. As shown in this paper, the analysis of drone reliability and its components is considered in studies often. Reliability analysis of drone swarms is investigated less often, despite the fact that many applications cannot be performed by a single drone and require the involvement of several drones. In this paper, a systematic review of the reliability analysis of drone swarms is proposed. Based on this review, a new method for the analysis and quantification of the topological aspects of drone swarms is considered. In particular, this method allows for the computing of swarm availability and importance measures. Importance measures in reliability analysis are used for system maintenance and to indicate the components (drones) whose fault has the most impact on the system failure. Structural and Birnbaum importance measures are introduced for drone swarms’ components. These indices are defined for the following topologies: a homogenous irredundant drone fleet, a homogenous hot stable redundant drone fleet, a heterogeneous irredundant drone fleet, and a heterogeneous hot stable redundant drone fleet. Full article

(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)

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