ON RELIABILITY FUNCTION OF A <i>K</i>-OUT-OF-<i>N</i> SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Rykov, Vladimir; Kozyrev, Dmitry; Filimonov, A. M.; Ivanova, Nika

doi:10.1017/s0269964820000285

Cited by 22 publications

(9 citation statements)

References 28 publications

(40 reference statements)

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“…The dominant variables can be further studied using other types of SA if the first moments [70], or the pdf shapes [90,91], or the importance of the components [92] are not explicitly known, as is often the case in engineering practice. Conversely, non-influential inputs can be fixed at any value of their domain without affecting Pf, usually close to the mean value.…”

Section: Discussionmentioning

confidence: 99%

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Kala

2021

Mathematics

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This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1-Pf) and discrete entropy—Pfln(Pf)-(1-Pf)ln(1-Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

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Section: Discussionmentioning

confidence: 99%

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Kala

2021

Mathematics

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“…The bibliography (on publications about these systems) is extensive (see Trivedi [1], Chakravarthy et al [2] and the bibliography therein). For a brief overview of further investigations on this topic, please see, for example, [3]. An overview of recent publications on k-out-of-n multi-state systems can be found in [4].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore it is fundamentally important to study the sensitivity of the system reliability indicators with respect to the shape of their unit lifetime distributions. Research in this direction can be found in a series of our papers, references to which one can find in chapter 9 of [34], as well as in [3]. For an overview of the recent research methods for queuing and reliability systems, one can find it in [35].…”

Section: Introductionmentioning

confidence: 99%

Preventive Maintenance of the k-out-of-n System with Respect to Cost-Type Criterion

2021

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In a previous paper, the problem of how the preventive maintenance organization for the k-out-of-n: F system could be used, in order to maximize system availability, was considered. The current paper continues these investigations using a different optimization criterion. The proposed approach is based on decision making theory for regenerative processes. We propose a general procedure for comparing different preventive maintenance strategies based on the ordered statistics distributions, aiming to choose the best one with respect to cost-type criterion. The lifetime distributions of system units are usually unknown and only one or two of their moments are available. For this reason, we pay special attention to the sensitivity analysis of decision making about preventive maintenance, taking into account the shape of the system unit lifetime distributions. A numerical study of two examples based on a real-world system illustrates the results of the proposed approach.

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“…The literature on such studies is vast (see for example Trivedi [12], Chakravarthy et al [13] and the bibliography therein). The bibliography of later studies can be found in, e.g., in [14]. Most of these investigations deal with the systems under assumptions about components' Poisson failure flow and exponential distribution of their repair time.…”

Section: Introductionmentioning

confidence: 99%

“…In the series of our previous works, the bibliography of which one can find for example in [14], for an investigation of a renewable k-out-of-n system with the Poisson flow of its components' failures and their arbitrarily distributed repair times, the socalled Markovization method was used. The method consists of the introduction of supplementary variables that allows describing the system behavior by a two-dimensional Markov process.…”

Section: Introductionmentioning

confidence: 99%

Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems

2021

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This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k-out-of-n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the first time: the partial and the full system repair scenarios. For both scenarios, the time-dependent system state probabilities are calculated in terms of their Laplace transforms. The closed form representation of the stationary probabilities for both scenarios are also presented. These latest results represent a new contribution to the study of this system.

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ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Cited by 22 publications

References 28 publications

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Preventive Maintenance of the k-out-of-n System with Respect to Cost-Type Criterion

Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems

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