A sequential order statistics approach to step-stress testing

Kamps, Udo; Kateri, Maria

doi:10.1007/s10463-010-0309-2

Cited by 36 publications

(9 citation statements)

References 24 publications

(29 reference statements)

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“…The presented approach could be transferred to related sequential order statistics models. In accelerated life-testing, for example, sequential order statistics serve as a step-stress model with proportional hazard rates and pre-specified numbers of observations under all stress levels (see [34], [35], [36]). Here, the model parameters associated with the stress levels are supposed to be connected via some parametric link function which allows for estimating the parameter corresponding to the stress under normal operating conditions based on data obtained from higher stress levels.…”

Section: Discussionmentioning

confidence: 99%

Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

Mies

Bedbur

2020

IEEE Trans. Rel.

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As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in reliability applications. By exploiting the probabilistic structure of sequential order statistics, we derive exact finite sample inference procedures to test for the load-sharing parameters and for the nonparametrically specified baseline distribution, treating the respective other part as a nuisance quantity. This improves upon previous approaches for the model, which either assume a fully parametric specification or rely on asymptotic results. Simulations show that the tests derived are able to detect deviations from the null hypothesis at small sample sizes. Critical values for a prominent case are tabulated.

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Section: Discussionmentioning

confidence: 99%

Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

Mies

Bedbur

2020

IEEE Trans. Rel.

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“…On the one hand, by appropriately setting the model parameters, the presented tests may be applied to check for identical scale parameters of underlying lifetime distributions in differently designed progressively type-II censored lifetime experiments ( see, e.g., Reference [28]). On the other hand, by choosing a standard exponential baseline distribution, we may test for equality of parameters associated with stress levels in multiple repeated type-II censored exponential step-stress experiments (see Reference [29]).…”

Section: Discussionmentioning

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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“…For further details on sequential order statistics, in particular concerning statistical inference, we refer to, e.g., Kamps (2006), Cramer and Kamps (1996, 2001a,b, 2003, Balakrishnan, Beutner and Kamps (2008), Beutner (2008Beutner ( , 2010, Kamps (2009), Burkschat (2009), Burkschat andLenz (2009), Bedbur (2010), Bedbur, Beutner and Kamps (2012), Burkschat, Kamps and Kateri (2010), and Balakrishnan, Kamps and Kateri (2012).…”

Section: Statistical Model and Preliminariesmentioning

confidence: 99%