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Likelihood Inference for the Lifetime Performance Index under Progressive Type-II Censoring

Author

Listed:
  • Laumen Benjamin

    (Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany)

  • Cramer Erhard

    (Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany)

Abstract

Likelihood inference for the lifetime performance index CL is discussed in the presence of progressive censoring. We illustrate that many results available in the literature can be traced back to the exponential case using appropriate transformations of the data. Further, we present procedures to compute the MLE of CL under the assumption of gamma distributed lifetimes. The results are illustrated by a simulation study and applied to a data set.

Suggested Citation

  • Laumen Benjamin & Cramer Erhard, 2015. "Likelihood Inference for the Lifetime Performance Index under Progressive Type-II Censoring," Stochastics and Quality Control, De Gruyter, vol. 30(2), pages 59-73, December.
    • Handle: RePEc:bpj:ecqcon:v:30:y:2015:i:2:p:59-73:n:3
    DOI: 10.1515/eqc-2015-0008
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    References listed on IDEAS

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    1. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    2. Mahmoud Mohamed Abdul Wahab & El-Sagheer Rashad Mohamed & Soliman Ahmed Abo-Elmagd & Abd Ellah Ahmed Hamed, 2014. "Inferences of the Lifetime Performance Index with Lomax Distribution Based on Progressive Type-II Censored Data," Stochastics and Quality Control, De Gruyter, vol. 29(1), pages 39-51, June.
    3. Wen-Chuan Lee, 2011. "Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max -value method," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 931-937.
    4. 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.
    5. 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.
    6. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    7. Lee, Wen-Chuan & Wu, Jong-Wuu & Hong, Ching-Wen, 2009. "Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2167-2179.
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