Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

Lauren Sauer, Yuhlong Lio and Tzong-Ru Tsai
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Lauren Sauer: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan

Mathematics, 2020, vol. 8, issue 7, 1-14

Abstract: In this paper, the reliability of a k -component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability.

Keywords: bootstrap procedure; delta method; maximum likelihood estimation; stress-strength (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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