Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative

Bedbur, Stefan; Müller, N.; Kamps, Udo

doi:10.1080/02331888.2015.1094070

Cited by 6 publications

(1 citation statement)

References 17 publications

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“…Estimators of model parameters or distribution parameters of the baseline cdf of SOSs are provided in, e.g., References [3][4][5][6][7][8][9][10]. Statistical tests for single or vectors of the model or baseline-distribution parameters of SOSs are proposed in References [3,6,7,[11][12][13], which, in particular, allow for model selection in the sense of whether order statistics have to be rejected for modelling in a given situation. More inferential results, along with the detailed model and structural properties, can be found in Reference [14].…”

Section: Introductionmentioning

confidence: 99%

Testing for Equality of Parameters from Different Load-Sharing Systems

Bedbur

Kamps

2019

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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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