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Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure

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  • Soumya Roy
  • Chiranjit Mukhopadhyay

Abstract

This article presents frequentist inference of accelerated life test data of series systems with independent log-normal component lifetimes. The means of the component log-lifetimes are assumed to depend on the stress variables through a linear stress translation function that can accommodate the standard stress translation functions in the literature. An expectation–maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters. The maximum likelihood estimates are then further refined by bootstrap, which is also used to infer about the component and system reliability metrics at usage stresses. The developed methodology is illustrated by analyzing a real as well as a simulated dataset. A simulation study is also carried out to judge the effectiveness of the bootstrap. It is found that in this model, application of bootstrap results in significant improvement over the simple maximum likelihood estimates.

Suggested Citation

  • Soumya Roy & Chiranjit Mukhopadhyay, 2015. "Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure," Journal of Risk and Reliability, , vol. 229(2), pages 119-130, April.
    • Handle: RePEc:sae:risrel:v:229:y:2015:i:2:p:119-130
    DOI: 10.1177/1748006X14565841
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    References listed on IDEAS

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    1. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    2. Soumya Roy & Chiranjit Mukhopadhyay, 2014. "Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2429-2451, May.
    3. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
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