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Properties of the Weibull cumulative exposure model

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  • Yoshio Komori

Abstract

This article is aimed at the investigation of some properties of the Weibull cumulative exposure model on multiple-step step-stress accelerated life test data. Although the model includes a probabilistic idea of Miner's rule in order to express the effect of cumulative damage in fatigue, our result shows that the application of only this is not sufficient to express degradation of specimens and the shape parameter must be larger than 1. For a random variable obeying the model, its average and standard deviation are investigated on a various sets of parameter values. In addition, a way of checking the validity of the model is illustrated through an example of the maximum likelihood estimation on an actual data set, which is about time to breakdown of cross-linked polyethylene-insulated cables.

Suggested Citation

  • Yoshio Komori, 2006. "Properties of the Weibull cumulative exposure model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(1), pages 17-34.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:1:p:17-34
    DOI: 10.1080/02664760500389475
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    References listed on IDEAS

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    1. Sang-Jun Park & Bong-Jin Yum, 1998. "Optimal design of accelerated life tests under modified stress loading methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 41-62.
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