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Estimation of reliability in a parallel system with random sample size. (English) Zbl 1259.62091

Summary: We derive the distribution of the life length of a parallel system with a random number of components when the life distribution of each component follows a Weibull distribution and the number of components follows a Poisson distribution truncated at zero. For two independent such parallel systems, we are interested in the estimation of the reliability parameter \(R = P(X > Y)\), where \(X\) and \(Y\) are the life lengths of the two parallel systems. The point estimate and confidence interval of \(R\), based on the maximum likelihood method, are developed. The performance of each of the point estimate and confidence interval of \(R\) is studied through an extensive simulation study. A numerical example, based on a real data, is presented to illustrate the implementation of the proposed procedure.

MSC:

62N05 Reliability and life testing
62F10 Point estimation
62F25 Parametric tolerance and confidence regions
65C60 Computational problems in statistics (MSC2010)
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References:

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