Reliability analysis of load-sharing systems with memory

Abstract

The load-sharing model has been studied since the early 1940s to account for the stochastic dependence of components in a parallel system. It assumes that, as components fail one by one, the total workload applied to the system is shared by the remaining components and thus affects their performance. Such dependent systems have been studied in many engineering applications which include but are not limited to fiber composites, manufacturing, power plants, workload analysis of computing, software and hardware reliability, etc. Many statistical models have been proposed to analyze the impact of each redistribution of the workload; i.e., the changes on the hazard rate of each remaining component. However, they do not consider how long a surviving component has worked for prior to the redistribution. We name such load-sharing models as memoryless. To remedy this potential limitation, we propose a general framework for load-sharing models that account for the work history. Through simulation studies, we show that an inappropriate use of the memoryless assumption could lead to inaccurate inference on the impact of redistribution. Further, a real-data example of plasma display devices is analyzed to illustrate our methods.

Reliability analysis of load-sharing systems with spatial dependence and proximity effects

“…Most of the recent studies on load sharing systems focus on the determination of reliability or availability function, statistical inference, and maintenance of systems with equal load-sharing, very few are focused on local-load sharing. Some recent works have been conducted on systems with equal load sharing (Zhang et al, 2017;Zhao et al, 2018;Asha et al, 2018;Wang et al, 2019;Zhang et al, 2019;De Paula et al, 2019;Franco et al, 2020;Zhang et al, 2020;Sharifi et al, 2021). In contrast, only a handful of recent works have looked at reliability study on local load-sharing problems (Guo et al, 2020).…”

“…Monotone loadsharing rule indicates that the load on the working components is non-decreasing even after the repair of the failed component (Suprasad et al, 2008) while local load-sharing rule implies that the load on a failed component is transferred to adjacent components (Kvam and Peña, 2005). Since the first work on load-sharing systems by Daniels (1945), a considerable number of studies have appeared in literature to investigate load-sharing systems for reliability assessment (Wang et al, 2019;Franco et al, 2020;Zhang et al, 2020), and maintenance optimization (Taghipour and Kassaei, 2015;Wang et al, 2015;Zhang et al, 2017).…”

Spreading of Failures in Small-World Networks: A Connectivity-Dependent Load Sharing Fibre Bundle Model

“…It offers a flexible approach to study how multicomponent systems evolve under varying load [2][3][4][5][6][7][8]. The flexibility refers to such aspects as: a) range and symmetry of interactions among units [9], b) rate of load's variation, c) heterogeneity/uniformity of units [10,11]), or d) varying quality of units [12,13], to name a few. The aspects a) and b) especially refer to ingredients of the FBM that play a major role when a given system is mapped onto a bundle of interacting fibers [14].…”

Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization Algorithm

“…Singh et al [7] presented a more generalized load-sharing system under an assumption of a constant hazard at the beginning and a linearly increasing hazard rate after the failure of several components. Wang et al [8] studied a more generalized load-sharing system with the work history or memory.…”