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Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions

Author

Listed:
  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Ehab M. Almetwally

    (Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 12613, Egypt
    Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Talkha 7730103, Egypt)

  • Qiuchen Hai

    (Department of Mathematical, Physical, and Engineering Sciences, Texas A&M University-San Antonio, San Antonio, TX 78224, USA)

  • Hoda Rezk

    (Department of Statistics, Al-Azhar University, Cairo 4434003, Egypt)

Abstract

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknown parameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique.

Suggested Citation

  • Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4652-:d:997531
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    References listed on IDEAS

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