On Stochastic Comparisons for Load-Sharing Series and Parallel Systems

Abstract

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning, however, the corresponding additional assumptions are not obvious, which can be seem from the proofs of our theorems.

Stochastic comparison on load‐sharing systems with one statistically dependent redundancy

“…Later, by using the model tackling age conversion in accelerated life tests, Yun and Cha 18 considered a load‐sharing parallel system with two absolutely continuous component lifetimes, derived the corresponding system reliability function, and investigated the workload allocation for some particular component lifetime such as the exponential and Weibull distributions. Unlike the predetermined workload setting in Yun and Cha, 18 Finkelstein and Hazra 19 recently studied the redundancy component allocation for load‐sharing series or parallel systems with the base and redundancy components following the load‐sharing model, and, under the assumption of the independence among component lifetimes, it is proved that allocating the redundancy component to the stochastically weakest (strongest) component of a series (parallel) system is the optimal strategy.…”

“…This article aims to partially fill this blank in the study of load‐sharing redundancy by taking into consideration the statistical dependence between the base and redundancy component lifetimes. As in the context of Finkelstein and Hazra, 19 the method in accelerated lifetime testing model is employed to describe the aging behavior of system components functioning in the regime that workload changes from the partial to the full. Moreover, in the present framework, the base and redundancy components follow the load‐sharing model, and also their lifetimes are assumed statistically dependent when they operate under the partial workload.…”

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.…”