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Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data

Author

Listed:
  • Mazen Nassar

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ahmed Elshahhat

    (Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt)

Abstract

In life-testing investigations, accelerated life testing is crucial since it reduces both time and costs. In this study, constant-stress partially accelerated life tests using adaptive progressively Type I censored samples are taken into account. This is accomplished under the assumption that the lifespan of products under normal use conditions follows the inverse Weibull distribution. In addition to using the maximum likelihood approach, the maximum product of the spacing procedure is utilized to obtain the point and interval estimates of the model parameters as well as the acceleration factor. Employing the premise of independent gamma priors, the Bayes point estimates using the squared error loss function and the Bayes credible intervals are obtained based on both the likelihood and product of spacing functions via the Markov chain Monte Carlo technique. To assess the effectiveness of the various approaches, a simulation study is used because it is not possible to compare the findings theoretically. To demonstrate the applicability of the various approaches, two real datasets for the lifetime of micro-droplets in the ambient environment and light-emitting diode failure data are investigated. Based on the numerical results, to estimate the parameters and acceleration factor of the inverse Weibull distribution based on the suggested scheme with constant-stress partially accelerated life tests, it is recommended to utilize the Bayesian estimation approach.

Suggested Citation

  • Mazen Nassar & Ahmed Elshahhat, 2023. "Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data," Mathematics, MDPI, vol. 11(2), pages 1-29, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:370-:d:1031288
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    References listed on IDEAS

    as
    1. Sanku Dey & Mazen Nassar, 2020. "Classical methods of estimation on constant stress accelerated life tests under exponentiated Lindley distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 975-996, April.
    2. Abdel-Hamid, Alaa H. & AL-Hussaini, Essam K., 2009. "Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1328-1338, February.
    3. Lin, Chien-Tai & Chou, Cheng-Chieh & Huang, Yen-Lung, 2012. "Inference for the Weibull distribution with progressive hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 451-467.
    4. Mazen Nassar & Farouq Mohammad A. Alam, 2022. "Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring," Mathematics, MDPI, vol. 10(5), pages 1-26, March.
    5. Abdullah Ali H. Ahmadini & Wali Khan Mashwani & Rehman Ahmad Khan Sherwani & Shokrya S. Alshqaq & Farrukh Jamal & Miftahuddin Miftahuddin & Kamran Abbas & Faiza Razaq & Mohammed Elgarhy & Sanaa Al-Mar, 2021. "Estimation of Constant Stress Partially Accelerated Life Test for Fréchet Distribution with Type-I Censoring," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, May.
    6. Suparna Basu & Sanjay K. Singh & Umesh Singh, 2019. "Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1377-1394, December.
    7. Sanku Dey & Liang Wang & Mazen Nassar, 2022. "Inference on Nadarajah–Haghighi distribution with constant stress partially accelerated life tests under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(11), pages 2891-2912, August.
    8. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
    9. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
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    1. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.

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