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Abstract
In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k-out-of-n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures.
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Bedbur S, Müller N, Kamps U. Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative. STATISTICS-ABINGDON 2015. [DOI: 10.1080/02331888.2015.1094070] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Bedbur S, Beutner E, Kamps U. Multivariate testing and model-checking for generalized order statistics with applications. STATISTICS-ABINGDON 2013. [DOI: 10.1080/02331888.2013.841696] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Shafay AR, Balakrishnan N, Sultan KS. Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2012.718779] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Schenk N, Burkschat M, Cramer E, Kamps U. Bayesian estimation and prediction with multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions. J Stat Plan Inference 2011. [DOI: 10.1016/j.jspi.2010.11.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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