Stochastic order for redundancy allocations in series and parallel systems

In this paper, we study stochastic comparisons of the coherent systems obtained under different repair policies. We consider minimal repairs of the components, that is, a failed component is replaced by another component which is similar (ie, it has the same distribution) to the replaced one and with the same age. Under these assumptions, we study how to determine the best replacement policies. Two general methods are proposed, one for systems with identically distributed components and another one for systems with ordered (in different stochastic senses) components. Both methods can be applied to systems with independent or dependent components. We use these methods to determine the optimal repair policies in some particular cases. We pay special attention to series and parallel systems with independent or dependent components. An algorithm to find the optimal replacement policy (when it exists) is provided.

Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of replacement policies in coherent systems under minimal repair

Arriaza

Navarro

Suárez‐Llorens

2018

“…As an important and popular fault tolerant structure, the k ‐out‐of‐ n system has been studied extensively in the past several decades. For this structure with system components having independent and stochastically ordered lifetimes and a single active redundancy, took the first to investigate the redundancy allocation and found that the active redundancy should be allocated to the weaker component so as to enhance the system reliability. Later, for a series system with two components' lifetimes and one active redundancy lifetime having independent exponential distributions, showed that allocating the redundancy to the weaker component lowers the system hazard rate.…”

Section: Symmetric Systems With Sai Components' Lifetimesmentioning

confidence: 99%

“…Due to the complexity of the corresponding optimization problem, most of these studies focus only on some specific structures with components having statistically independent lifetimes. For example, studied the optimal allocation strategy for series and parallel systems with active redundancies. Mi , further investigated the optimal policy to allocate multiple active redundancies to a k ‐out‐of‐ n system.…”

Section: Introductionmentioning

confidence: 99%

On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes

Fang

2016

This article studies coherent systems of heterogenous and statistically dependent components' lifetimes. We present a sufficient and necessary condition for a stochastically longer system lifetime resulted by allocating a single active redundancy. For exchangeable components' lifetimes, allocating the redundancy to the component with more minimal path sets is proved to produce a more reliable system, and for systems with stochastic arrangement increasing components' lifetimes and symmetric structure with respect to two components, allocating the redundancy to the weaker one brings forth a larger reliability. Several numerical examples are presented to illustrate the theoretical results as well. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 335–345, 2016

“…Boland et al established that, if X 1 is smaller than X 2 in terms of the hazard rate order, then the standby redundancy is more favorable with component C 1 than with component C 2 , that is,

X_{1} \leq_{hr} X_{2} \Rightarrow \land (X_{1} + X, X_{2}) \geq_{st} \land (X_{1}, X_{2} + X) .

…”

Section: Allocation Of Standby Redundanciesmentioning

confidence: 99%

“…In this regard, the allocation of the redundant component(s) in a system to optimize the lifetime of that system is of great interest in reliability engineering and system security. This topic has given rise to many interesting theoretical problems on which a number of researchers have focused their attention in the past few decades; see, for example, and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Allocation of two redundancies in two-component series systems

Zhao

Chan

et al. 2013

The allocation of redundancies in a system to optimize the reliability of system performance is an interesting problem in reliability engineering and system security. In this article, we focus on the optimal allocation of two exponentially distributed active (standby) redundancies in a two‐component series system using the tool of stochastic ordering. For the case of active redundancy, stochastic comparisons are carried out in terms of the likelihood ratio and reversed hazard rate orders. For the case of standby redundancy, a likelihood ratio ordering result is developed. The results established here generalize and strengthen corresponding results in the recent literature. In addition, several numerical examples are used to explicate the results. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013