The prediction of remaining useful lifetime for the Weibull k-out-of-n load-sharing system

In this paper, the prediction intervals of the off-line and online remaining useful lifetimes for the k-out-of -n load-sharing system is studied under the equal load-sharing rule. When the lifetime of each component follows the Weibull distribution, the maximum likelihood estimators and two-stage estimators of the model parameters, system reliability and mean lifetime are proposed. The Wald and bootstrap-type confidence intervals for the model parameters are developed. The performance of the proposed prediction intervals is assessed by using Monte Carlo simulation. The simulation results indicate that the coverage probabilities of the proposed bootstrap-type prediction intervals are close to the nominal confidence levels even if the sample size is small. A real example is utilized to illustrate the proposed bootstrap-type prediction interval methods.