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.

Semiparametric inference for a general class of models for recurrent events

“…This will be the topic of another paper, and the resolution of this asymptotic problem may require empirical process methods utilized in Murphy (1994Murphy ( , 1995 and Parner (1998); see also the recent paper of Kosorok et al (2004). Some asymptotic results for specific models subsumed by the general class of models could be found in Peña et al (2001) and Kvam and Peña (2005). Through such asymptotic analysis we will be able to obtain expressions for approximating analytically the standard errors of the estimators which will reflect the effects of an informative right-censoring mechanism as well as the impact of the sum-quota accrual scheme (see Peña et al (2001) for the special case of a renewal model).…”

“…A popular load-sharing model is the equal load-share model considered in Kvam and Peña (2005). One context is a -component parallel system consisting of identical components, for which the event of interest is the occurrence of a component failure.…”

Maintenance analysis of a two-component load-sharing system

“…For instance, one can enumerate the sensors which take the workload together in a distributed computer system; the pumps sharing the workload in a hydraulic system; the welded joints in a bridge support [36]; the cables in a suspension bridge system [37] and the hoisting ropes in the mining system. Hoisting rope plays a significant role in mining system as its tensile strength and lifetime affect directly the system reliability and the system operation state.…”

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

“…This factor is a change of working conditions of systems that is caused by a change of the load on the system and its components. A clear example illustrating the impact of the changeable load is provided by Kvam and Peña [1]. The authors of this work describe a large structure supported by welded joints.…”