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On sensitivity analysis of aging multi-state system by using LZ-transform

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  • Lisnianski, Anatoly
  • Frenkel, Ilia
  • Khvatskin, Lev

Abstract

The paper considers a sensitivity evaluation for an aging multi-state system (MSS) under minimal repair. Investigation of an impact of changing different failure/repair rates of different elements in MSS is important for practical reliability engineering. In practical reliability engineering a "curse of dimensionality" (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for sensitivity assessment. Straightforward Markov Method applied to solve this problem requires building a model with numerous numbers of states and solving a corresponding system of differential equations. In order to solve this problem, the paper proposes to use a new method based on an LZ-transform of the discrete-state continuous-time Markov process, and on Ushakov's Universal Generating Operator. New sensitivity measures useful for aging MSS reliability analysis were introduced. It was shown that the proposed method drastically reduces a computational burden. A numerical example is presented in order to illustrate the approach.

Suggested Citation

  • Lisnianski, Anatoly & Frenkel, Ilia & Khvatskin, Lev, 2017. "On sensitivity analysis of aging multi-state system by using LZ-transform," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 99-108.
    • Handle: RePEc:eee:reensy:v:166:y:2017:i:c:p:99-108
    DOI: 10.1016/j.ress.2016.12.001
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    References listed on IDEAS

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    1. Peng, Rui & Zhai, Qingqing & Xing, Liudong & Yang, Jun, 2014. "Reliability of demand-based phased-mission systems subject to fault level coverage," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 18-25.
    2. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
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    Cited by:

    1. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
    2. Xiao, Hui & Zhang, Yiyun & Xiang, Yisha & Peng, Rui, 2020. "Optimal design of a linear sliding window system with consideration of performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 198(C).

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