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Exact Likelihood-Ratio Tests for a Simple Step-Stress Cumulative Exposure Model with Censored Exponential Data

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  • Xiaojun Zhu

    (Xi’an Jiaotong-Liverpool University)

  • N. Balakrishnan

    (McMaster University)

  • Yiliang Zhou

    (WuXi AppTec (Suzhou) Co., Ltd.)

Abstract

An accelerated life test (ALT) is commonly used in reliability studies of high quality products. A step-stress experiment is one such ALT that is often used in practice. In this paper, we develop exact inference based on likelihood-ratio test for a simple step-stress model with exponential lifetimes under Type-II censoring. We consider both unrestricted and order-restricted maximum likelihood estimators (MLEs) for this purpose. We also derive the exact power function of this test, which we then use for designing an optimal step-stress testing experiment. By using a similar approach, we extend these results to other forms of censoring. Monte Carlo simulations are then carried out to evaluate the performance of the inferential methods developed here. Finally, an illustrative example is presented for demonstrating all the inferential results.

Suggested Citation

  • Xiaojun Zhu & N. Balakrishnan & Yiliang Zhou, 2020. "Exact Likelihood-Ratio Tests for a Simple Step-Stress Cumulative Exposure Model with Censored Exponential Data," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 497-509, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09719-3
    DOI: 10.1007/s11009-019-09719-3
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    References listed on IDEAS

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    1. Morris H. Degroot & Prem K. Goel, 1979. "Bayesian estimation and optimal designs in partially accelerated life testing," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 223-235, June.
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    Cited by:

    1. Mao Song & Liu Bin & Shi Yimin, 2021. "Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-I Hybrid Censoring," Journal of Systems Science and Information, De Gruyter, vol. 9(5), pages 533-548, October.
    2. Xiaojun Zhu & Narayanaswamy Balakrishnan & Hon-Yiu So, 2022. "Exact One- and Two-Sample Likelihood Ratio Tests based on Time-Constrained Life-Tests from Exponential Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2009-2028, September.

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