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 γ1r (t), then to γ2r (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.

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Copyright © 2005 Taylor & Francis

DOI: 10.1198/016214504000000863

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Kvam, Paul H., and Edsel A. Peña. "Estimating Load-Sharing Properties in a Dynamic Reliability System." Journal of the American Statistical Association 100, no. 469 (2005): 262-272. doi:10.1198/016214504000000863.