Testing for Equality of Parameters from Different Load-Sharing Systems

Stefan Bedbur and Udo Kamps
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Stefan Bedbur: Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany
Udo Kamps: Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany

Stats, 2019, vol. 2, issue 1, 1-19

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.

Keywords: reliability; k -out-of- n system; load-sharing system; order statistics; sequential order statistics; likelihood-ratio test; Rao score test (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2019
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