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Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme

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  • Hon Keung Tony Ng
  • Debasis Kundu
  • Ping Shing Chan

Abstract

In this article, a mixture of Type‐I censoring and Type‐II progressive censoring schemes, called an adaptive Type‐II progressive censoring scheme, is introduced for life testing or reliability experiments. For this censoring scheme, the effective sample size m is fixed in advance, and the progressive censoring scheme is provided but the number of items progressively removed from the experiment upon failure may change during the experiment. If the experimental time exceeds a prefixed time T but the number of observed failures does not reach m, we terminate the experiment as soon as possible by adjusting the number of items progressively removed from the experiment upon failure. Computational formulae for the expected total test time are provided. Point and interval estimation of the failure rate for exponentially distributed failure times are discussed for this censoring scheme. The various methods are compared using Monte Carlo simulation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Suggested Citation

  • Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:8:p:687-698
    DOI: 10.1002/nav.20371
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    1. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    2. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
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    1. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.
    2. Hassan Okasha & Yuhlong Lio & Mohammed Albassam, 2021. "On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme," Mathematics, MDPI, vol. 9(22), pages 1-38, November.
    3. Siqi Chen & Wenhao Gui, 2020. "Estimation of Unknown Parameters of Truncated Normal Distribution under Adaptive Progressive Type II Censoring Scheme," Mathematics, MDPI, vol. 9(1), pages 1-33, December.
    4. 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.
    5. EL-Sayed A. El-Sherpieny & Ahmed Elshahhat & Nader M. Abdallah, 2024. "Statistical Analysis of Improved Type-II Adaptive Progressive Hybrid Censored NH Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 721-754, August.
    6. Abdalla Abdel-Ghaly & Hanan Aly & Elham Abdel-Rahman, 2023. "Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 132-174, May.
    7. O. E. Abo-Kasem & Ehab M. Almetwally & Wael S. Abu El Azm, 2023. "Inferential Survival Analysis for Inverted NH Distribution Under Adaptive Progressive Hybrid Censoring with Application of Transformer Insulation," Annals of Data Science, Springer, vol. 10(5), pages 1237-1284, October.
    8. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    9. Muqrin A. Almuqrin & Mukhtar M. Salah & Essam A. Ahmed, 2022. "Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications," Mathematics, MDPI, vol. 10(22), pages 1-38, November.
    10. Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    11. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    12. Refah Alotaibi & Mazen Nassar & Ahmed Elshahhat, 2022. "Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    13. Shuhan Liu & Wenhao Gui, 2020. "Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks," Mathematics, MDPI, vol. 8(10), pages 1-16, October.

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