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Barakat HM, El-Adll ME, Aly AE. Two-sample nonparametric prediction intervals based on random number of generalized order statistics. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1719421] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- H. M. Barakat
- Department of Mathematics-Faculty of Science, Zagazig University, Zagazig, Egypt
| | - Magdy E. El-Adll
- Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt
| | - Amany E. Aly
- Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt
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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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