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Optimal Robust Designs of Step-Stress Accelerated Life Testing Experiments for Proportional Hazards Models

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

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  • Xaiojian Xu

    (Brock University, Department of Mathematics and Statistics)

  • Wan Yi Huang

    (Brock University, Department of Mathematics and Statistics)

Abstract

Accelerated life testing (ALT) is broadly used to obtain reliability information of a product in a timely manner. The Cox’s proportional hazards (PH) model is often utilized for reliability analysis. In this paper, we focus on designing ALT experiments for hazard rate prediction when a PH model is adopted. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model can not be tested. For possible imprecision in an assumed PH model, the method of construction for robust designs is explored. As an example, we investigate the robust designs for the situation where baseline hazard function in the fitted PH model is simple linear but the true baseline hazard function is actually quadratic. The optimal stress-changing times are determined by minimizing the asymptotic variance and asymptotic squared bias.

Suggested Citation

  • Xaiojian Xu & Wan Yi Huang, 2016. "Optimal Robust Designs of Step-Stress Accelerated Life Testing Experiments for Proportional Hazards Models," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 585-594, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_53
    DOI: 10.1007/978-3-319-30379-6_53
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