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Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution

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  • Cheng‐Hung Hu
  • Robert D. Plante
  • Jen Tang

Abstract

Accelerated life testing (ALT) is commonly used to obtain reliability information about a product in a timely manner. Several stress loading designs have been proposed and recent research interests have emerged concerning the development of equivalent ALT plans. Step‐stress ALT (SSALT) is one of the most commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This article considers two fundamental questions when designing a SSALT and provides formal proofs in answer to each. Namely: (1) can a simple SSALT be designed so that it is equivalent to other stress loading designs? (2) when optimizing a multilevel SSALT, does it degenerate to a simple SSALT plan? The answers to both queries, under certain reasonable model assumptions, are shown to be a qualified YES. In addition, we provide an argument to support the rationale of a common practice in designing a SSALT, that is, setting the higher stress level as high as possible in a SSALT plan. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Suggested Citation

  • Cheng‐Hung Hu & Robert D. Plante & Jen Tang, 2013. "Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 19-30, February.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:1:p:19-30
    DOI: 10.1002/nav.21516
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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.
    2. H. K. T. Ng & N. Balakrishnan & P. S. Chan, 2007. "Optimal sample size allocation for tests with multiple levels of stress with extreme value regression," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(3), pages 237-249, April.
    3. Haitao Liao & Elsayed A. Elsayed, 2010. "Equivalent accelerated life testing plans for log‐location‐scale distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 472-488, August.
    4. Do Sun Bai & Myung Soo Kim, 1993. "Optimum simple step‐stress accelerated life tests for weibull distribution and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 193-210, March.
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    Cited by:

    1. David Han & H.K.T. Ng, 2013. "Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 541-556, October.
    2. Yan, Weian & Xu, Xiaofan & Bigaud, David & Cao, Wenqin, 2023. "Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. Han, David & Bai, Tianyu, 2020. "Design optimization of a simple step-stress accelerated life test – Contrast between continuous and interval inspections with non-uniform step durations," Reliability Engineering and System Safety, Elsevier, vol. 199(C).

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