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Estimation of the reliability of a stress-strength system from power Lindley distributions. (English) Zbl 1325.62048
Summary: We are interested in the estimation of the reliability parameter \(R = P(X > Y)\) where \(X\), a component strength, and \(Y\), a component stress, are independent power Lindley random variables. The point and interval estimation of \(R\), based on maximum likelihood, nonparametric and parametric bootstrap methods, are developed. The performance of the point estimate and confidence interval of \(R\) under the considered estimation methods is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the proposed procedure.

MSC:
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F40 Bootstrap, jackknife and other resampling methods
62F15 Bayesian inference
62N05 Reliability and life testing
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