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Fisher information based progressive censoring plans

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  • Balakrishnan, N.
  • Burkschat, Marco
  • Cramer, Erhard
  • Hofmann, Glenn

Abstract

In life tests, the progressive Type-II censoring methodology allows for the possibility of censoring a number of units each time a failure is observed. This results in a large number of possible censoring plans, depending on the number of both censoring times and censoring numbers. Employing maximum Fisher Information as an optimality criterion, optimal plans for a variety of lifetime distributions are determined numerically. In particular, exact optimal plans are established for some important lifetime distributions. While for some distributions, Fisher information is invariant with respect to the censoring plan, results for other distributions lead us to hypothesize that the optimal scheme is in fact always a one-step method, restricting censoring to exactly one point in time. Depending on the distribution and its parameters, this optimal point of censoring can be located at the end (right censoring) or after a certain proportion of observations. A variety of distributions is categorized accordingly. If the optimal plan is a one-step censoring scheme, the optimal proportion is determined. Moreover, the Fisher information as well as the expected time till the completion of the experiment for the optimal one-step censoring plan are compared with the respective quantities of both right censoring and simple random sampling.

Suggested Citation

  • Balakrishnan, N. & Burkschat, Marco & Cramer, Erhard & Hofmann, Glenn, 2008. "Fisher information based progressive censoring plans," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 366-380, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:366-380
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    References listed on IDEAS

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    1. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
    2. U. H. Salemi & S. Rezaei & Y. Si & S. Nadarajah, 2018. "On Optimal Progressive Censoring Schemes for Normal Distribution," Annals of Data Science, Springer, vol. 5(4), pages 637-658, December.
    3. M. Razmkhah & S. Simriz, 2018. "Statistical inferences based on INID progressively type II censored order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 583-604, June.
    4. Erhard Cramer & George Iliopoulos, 2010. "Adaptive progressive Type-II censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 342-358, August.
    5. Park, Sangun & Ng, Hon Keung Tony & Chan, Ping Shing, 2015. "On the Fisher information and design of a flexible progressive censored experiment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 142-149.
    6. Uoseph Hamdi Salemi & Esmaile Khorram & Yuancheng Si & Saralees Nadarajah, 2020. "Sensitivity analysis of censoring schemes in progressively type-II right censored order statistics," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 163-189, March.
    7. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    8. Ritwik Bhattacharya, 2020. "Implementation of compound optimal design strategy in censored life-testing experiment," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1029-1050, December.
    9. Parsi, Safar & Bairamov, Ismihan, 2009. "Expected values of the number of failures for two populations under joint Type-II progressive censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3560-3570, August.
    10. Ritwik Bhattacharya & Biswabrata Pradhan, 2017. "Computation of optimum Type-II progressively hybrid censoring schemes using variable neighborhood search algorithm," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 802-821, December.
    11. Park, Sangun & Ng, Hon Keung Tony, 2012. "Missing information and an optimal one-step plan in a Type II progressive censoring scheme," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 396-402.
    12. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.
    13. Benjamin Laumen & Erhard Cramer, 2019. "Stage life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 632-647, December.
    14. Wu, Shuo-Jye & Huang, Syuan-Rong, 2012. "Progressively first-failure censored reliability sampling plans with cost constraint," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2018-2030.
    15. Elham Basiri & Jafar Ahmadi, 2013. "Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records," Computational Statistics, Springer, vol. 28(6), pages 2825-2848, December.
    16. Uoseph Hamdi Salemi & Sadegh Rezaei & Saralees Nadarajah, 2019. "A-optimal and D-optimal censoring plans in progressively Type-II right censored order statistics," Statistical Papers, Springer, vol. 60(4), pages 1349-1367, August.
    17. Ritwik Bhattacharya & Baidya Nath Saha & Graceila González Farías & Narayanaswamy Balakrishnan, 2020. "Multi-criteria-based optimal life-testing plans under hybrid censoring scheme," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 430-453, June.

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