Reliability modeling of weighted k-out-of-n systems exposed to external shocks

Hamed Lorvand and Somayeh Zarezadeh ()
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Hamed Lorvand: Isfahan University of Technology
Somayeh Zarezadeh: Shiraz University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 33, issue 1, No 6, 133-160

Abstract: Abstract Consider a system with n components where a positive integer-valued random weight is used to describe the capacity of each component. The system is assumed to be exposed to external shocks that arrive at random times, and each shock causes the failure of at least one component. Let the system function if at least k components work, and the total weight of working components is more than a threshold, say c. In this paper, a new concept named a shock-based signature (SBS) vector is introduced, which is free of the distribution function of the arrival times of the shocks. It depends only on the resistance probability of the components against the shocks and the system’s structure. Then, a representation is obtained for the reliability function of the considered system as a mixture of the reliability function of the arrival times of shocks with mixing distribution as SBS. The proposed shock model can be also employed for the usual k-out-of-n systems when $$c=0$$ c = 0 . An application of the model is also presented for the preventive maintenance policy of the considered system. To illustrate the results, some examples are numerically and graphically given.

Keywords: Weighted system; Preventive maintenance; Emergency repair; Non-homogeneous Poisson process; Cost function; 90B25; 60K10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11750-024-00681-z

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