Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Stochastic Comparison of ‏‎$‎‎‎k‎$‎-out-of-‎‏‎$‎‎‎n‎$‎ Systems‎‏ ‎Based ‎on‎ Distortion Function

Document Type : Original Paper

Authors
Elham Khaleghpanah Noughabi
Majid Rezaei
Majid Chahkandi
Department of Statistics, University of Birjand, Birjand, Iran
10.22055/jamm.2020.30655.1748
Abstract
One of the relevant problem in the reliability theory is stochastic comparison of coherent systems. Several results have been obtained in stochastic comparison of systems with independent and identically (IID) components. In this paper, we focus on $ k $-out-of-$ n $ systems that play an important role in study of the reliability of engineering systems. We obtain some results on distribution-free comparisons of $ k $-out-of-$ n $ systems, with possibly dependent component lifetimes, based on the concept of distortion function. We provide some conditions on distorted distributions of $ k $-out-of-$ n $ systems or their residual lifetimes that conclude ordering between their lifetimes ‎or their residual lifetimes‎. As a special case we consider two common survival copula (Farlie-Gumbel-Morgenstern and Clayton–Oakes) to derive more details on stochastic comparison of $ k $-out-of-$ n $ systems with respect to $ k $ and $ n $. Some illustrative examples are also presented to ‎show that some of results for stochastic comparison of $ k $-out-of-$ n $ systems with i.i.d ‎components ‎are violated ‎in ‎dependent ‎case.
Keywords
k-out-of-n system
Distortion function
Copula ‎function‎
Residual Lifetime
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Journal of Advanced Mathematical Modeling
Volume 10, Issue 2
December 2020
Pages 356-378

  • Receive Date 12 August 2019
  • Revise Date 08 May 2020
  • Accept Date 23 May 2020