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Fisher information based progressive censoring plans

Author

Listed:
  • 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. 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. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    3. Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
    4. Burkschat, M. & Cramer, E. & Kamps, U., 2006. "On optimal schemes in progressive censoring," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1032-1036, May.
    5. Gertsbakh, Ilya & Kagan, Abram, 1999. "Characterization of the Weibull distribution by properties of the Fisher information under type-I censoring," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 99-105, March.
    6. Hofmann, Glenn & Balakrishnan, N. & Ahmadi, Jafar, 2005. "Characterization of hazard function factorization by Fisher information in minima and upper record values," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 51-57, April.
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    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. Ritwik Bhattacharya & Biswabrata Pradhan & Anup Dewanji, 2016. "On optimum life-testing plans under Type-II progressive censoring scheme 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. 25(2), pages 309-330, June.
    5. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0598-9 is not listed on IDEAS
    6. 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.
    7. 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.
    8. repec:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0534-6 is not listed on IDEAS
    9. 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.
    10. 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.
    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.

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