Reliability Estimation Based on System Data with an Unknown Load Share Rule

Abstract

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) the system load is distributed evenly among the working components, and (2) we assume only the load for each working component increases when other components in the system fail. Tests for these special load-share models are investigated.

Estimating Load-Sharing Properties in a Dynamic Reliability System

“…For instance, the first term of this limiting variance function is given by Note that this expression is at most equal to which is the asymptotic variance function of the Nelson-Aalen estimator of R(s) which utilizes only the first component failure for each system. This estimator is given by (15) This particular result demonstrates that if γ is known, then the estimator is more efficient than the estimator , certainly not a surprising result. However, since γ is not known and is estimated to form the estimator , the second term in Ξ(s; γ) given by must be taken into account in comparing the asymptotic variances of and .…”

“…This is the monotone load share rule mentioned in Section 1. Kim and Kvam (2004) consider the simple case in which failure data follow an exponential distribution, and order restricted inference is used to estimate the load share rule under the monotone load share restriction.…”

Maintenance analysis of a two-component load-sharing system

“…Kim et al [25] proposed the classical maximum-likelihood estimation of the system parameters where all components have identical exponential distribution. Park et al [26] extended the model of Kim et al [25] by considering the parallel system with Weibull distributed lifetime distribution. The closed-form Maximum Likelihood Estimator and conditional Best Unbiased Estimator of the Weibull rate parameters are derived.…”

A Load-Share Reliability Model under the Changeable Piecewise Smooth Load

“…Daniels originally adopted the load-share model to describe how the strain on yarn fibers increases as individual fibers within a bundle break. Last decades, many authors contribute to the load-share models, for instance, Bebbington et al [6], Deshpande et al [7], Lee et al [8], Kim 2 Journal of Quality and Reliability Engineering and Kvam [9], Lynch [10], Ross [11], Shao and Lamberson [12], Stefanescu and Turnbull [13], and Yang and Younis [14].…”