Estimating Load-Sharing Properties in a Dynamic Reliability System

Abstract

An estimator for the load-share parameters in an equal load-share model is derived based on observing k -component parallel systems of identical components that have a continuous distribution function F (˙) and failure rate r (˙). In an equal load-share model, after the first of k components fails, failure rates for the remaining components change from r ( t ) to γ 1 r ( t ), then to γ 2 r ( t ) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline cumulative hazard function R = –log(1 – F ) is presented, and its asymptotic limit process is established to be a Gaussian process. The effect of estimation of the load-share parameters is considered in the derivation of the limiting process. Potential applications can be found in diverse areas, including materials testing, software reliability, and power plant safety assessment.