Optimal allocation of minimal repairs in parallel and series systems

Abstract

In reliability engineering, the concept of minimal repair describes that the repair brings the failed unit (eg, system or component) to the situation which is same as it was just before the failure. With the help of the well‐known Gamma‐Poisson relationship, this paper investigates optimal allocation strategies of minimal repairs for parallel and series systems through implementing stochastic comparisons of various allocation policies in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orderings. Numerical examples are presented to illustrate these findings as well. These results not only strengthen and generalize some known ones in the seminal work of Shaked and Shanthikumar, but also solve the open problems proposed by Chahkandi et al.'s study and Arriaza et al.'s study.

Comparisons on Largest Order Statistics From Heterogeneous Gamma Samples

“…Therefore, it is sufficient for us to prove that k(r, y) is decreasing in r ∈ R ++ and increasing in y ∈ R ++ , respectively, to make sure that equation ( 7) is nonpositive. Firstly, the decreasing property of k(r, y) with respect to r is proved by Theorem 3.2 of Zhang and Zhao [29].…”

“…, λ n ). Recently, by employing the Gamma-Poisson relationship, Zhang and Zhao [29] studied optimal allocation strategies of minimal repairs for parallel and series systems with i.i.d. components in the sense of the hazard rate, the reversed hazard rate and the likelihood ratio orderings.…”

“…Obviously, it contains exponential distribution as a special case when r = 1. Gamma distribution is also widely used to describe the lifetime of components in shock model or undergoing minimal repairs (see [18,25,29]). Let X 1 , X 2 , .…”

Optimal allocation of relevations in coherent systems

“…warranty coverage, integrated-circuit panels in a television set, and water pumps in a car), it might be more practical and more resource-saving to minimally repair the failed units so as to bring them back to the working state immediately before failure. For a more detailed study of the effect of minimal repair in reliability systems, one may refer to [1], [3], [23], and [38]. It will be stated later that relevation redundancy includes the minimal repair policy as a special case.…”

Reliability Comparison of Two Unit Redundancy Systems Under the Load Requirement

“…Previous research on design for reliability has typically considered the problem of allocating the redundancy for a given system configuration [16]. For example, the redundancy level was determined to maximize reliability of a series system for the cold standby [3,32,35] and the hot standby [14,19,20], whereas the optimal redundancy allocation strategy was developed for a load-sharing system [10] and a series system with [38] and without repair [40]. However, litter research has been done to compare the reliability functions of different redundancy configurations.…”