Progressive Hybrid and Adaptive Censoring and Related Inference

  • N. Balakrishnan
  • Erhard Cramer
Part of the Statistics for Industry and Technology book series (SIT)


Inferential results for progressive hybrid and adaptive progressive Type-II censored data are shown. A special focus is given to one- and two-parameter exponential distributions.


Maximum Likelihood Estimator Probability Mass Function Likelihood Inference Construct Confidence Interval Exact Confidence Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 45.
    Amin ZH (2008a) Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals. J Appl Stat 35:1203–1217CrossRefzbMATHMathSciNetGoogle Scholar
  2. 101.
    Balakrishnan N, Iliopoulos G (2009) Stochastic monotonicity of the MLE of exponential mean under different censoring schemes. Ann Inst Stat Math 61:753–772CrossRefzbMATHMathSciNetGoogle Scholar
  3. 108.
    Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications (with discussions). Comput Stat Data Anal 57:166–209CrossRefMathSciNetGoogle Scholar
  4. 127.
    Balakrishnan N, Varadan J (1991) Approximate MLEs for the location and scale parameters of the extreme value distribution with censoring. IEEE Trans Reliab 40:146–151CrossRefzbMATHGoogle Scholar
  5. 136.
    Balakrishnan N, Kannan N, Lin CT, Wu SJS (2004a) Inference for the extreme value distribution under progressive Type-II censoring. J Stat Comput Simul 74:25–45CrossRefzbMATHMathSciNetGoogle Scholar
  6. 156.
    Balakrishnan N, Cramer E, Iliopoulos G (2014) On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints. Stat Probab Lett 89:124–130CrossRefzbMATHMathSciNetGoogle Scholar
  7. 169.
    Barlow RE, Madansky A, Proschan F, Scheuer EM (1968) Statistical estimation procedures for the ‘burn-in’ process. Technometrics 10:51–62MathSciNetGoogle Scholar
  8. 210.
    Bobotas P, Kourouklis S (2011) Improved estimation of the scale parameter, the hazard rate parameter and the ratio of the scale parameters in exponential distributions: an integrated approach. J Stat Plan Infer 141:2399–2416CrossRefzbMATHMathSciNetGoogle Scholar
  9. 239.
    Casella G, Berger RL (2002) Statistical inference, 2nd edn. Duxbury Press, Pacific GroveGoogle Scholar
  10. 249.
    Chen SM, Bhattacharyya GK (1988) Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Stat Theory Meth 16:2429–2442CrossRefMathSciNetGoogle Scholar
  11. 259.
    Childs A, Chandrasekar B, Balakrishnan N, Kundu D (2003) Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 55:319–330zbMATHMathSciNetGoogle Scholar
  12. 260.
    Childs A, Chandrasekar B, Balakrishnan N (2008) Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhäuser, Boston, pp 323–334Google Scholar
  13. 261.
    Childs A, Balakrishnan N, Chandrasekar B (2012) Exact distribution of the MLEs of the parameters and of the quantiles of two-parameter exponential distribution under hybrid censoring. Statistics 46:441–458zbMATHMathSciNetGoogle Scholar
  14. 292.
    Cramer E, Balakrishnan N (2013) On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions. Stat Meth 10:128–150CrossRefMathSciNetGoogle Scholar
  15. 294.
    Cramer E, Iliopoulos G (2010) Adaptive progressive Type-II censoring. TEST 19:342–358CrossRefzbMATHMathSciNetGoogle Scholar
  16. 315.
    Cramer E, Burkschat M, Górny J (2014) On some exact distributional results based on Type-II progressively hybrid censored data from exponential distributions (submitted)Google Scholar
  17. 352.
    Epstein B (1954) Truncated life tests in the exponential case. Ann Math Stat 25:555–564CrossRefzbMATHGoogle Scholar
  18. 392.
    Ganguly A, Mitra S, Samanta D, Kundu D (2012) Exact inference for the two-parameter exponential distribution under Type-II hybrid censoring. J Stat Plan Infer 142:613–625CrossRefzbMATHMathSciNetGoogle Scholar
  19. 439.
    Hemmati F, Khorram E (2013) Statistical analysis of the log-normal distribution under Type-II progressive hybrid censoring schemes. Comm Stat Simul Comput 42:52–75CrossRefzbMATHMathSciNetGoogle Scholar
  20. 479.
    Joarder A, Krishna H, Kundu D (2009) On Type-II progressive hybrid censoring. J Mod Appl Stat Meth 8:534–546Google Scholar
  21. 503.
    Kamps U, Cramer E (2001) On distributions of generalized order statistics. Statistics 35:269–280CrossRefzbMATHMathSciNetGoogle Scholar
  22. 560.
    Kundu D, Joarder A (2006a) Analysis of Type-II progressively hybrid censored competing risks data. J Mod Appl Stat Meth 5:152–170Google Scholar
  23. 561.
    Kundu D, Joarder A (2006b) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528CrossRefzbMATHMathSciNetGoogle Scholar
  24. 565.
    Kundu D, Samanta D, Ganguly A, Mitra S (2013) Bayesian analysis of different hybrid and progressive life tests. Comm Stat Simul Comput 42:2160–2173CrossRefzbMATHGoogle Scholar
  25. 600.
    Lin CT, Huang YL (2012) On progressive hybrid censored exponential distribution. J Stat Comput Simul 82:689–709CrossRefzbMATHMathSciNetGoogle Scholar
  26. 607.
    Lin CT, Ng HKT, Chan PS (2009b) Statistical inference of Type-II progressively hybrid censored data with Weibull lifetimes. Comm Stat Theory Meth 38:1710–1729CrossRefzbMATHMathSciNetGoogle Scholar
  27. 610.
    Lin CT, Chou CC, Huang YL (2012) Inference for the Weibull distribution with progressive hybrid censoring. Comput Stat Data Anal 56:451–467CrossRefzbMATHMathSciNetGoogle Scholar
  28. 648.
    MIL-STD-781-C (1977) Reliability design qualification and production acceptance tests: exponential distribution. U.S. Government Printing Office, WashingtonGoogle Scholar
  29. 654.
    Mokhtari EB, Rad AH, Yousefzadeh F (2011) Inference for Weibull distribution based on progressively Type-II hybrid censored data. J Stat Plan Infer 141:2824–2838CrossRefzbMATHGoogle Scholar
  30. 690.
    Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme. Naval Res Logist 56:687–698CrossRefzbMATHMathSciNetGoogle Scholar
  31. 774.
    Sarhan AM, Al-Ruzaizaa A (2010) Statistical inference in connection with the Weibull model using Type-II progressively censored data with random scheme. Pakistan J Stat 26:267–279MathSciNetGoogle Scholar
  32. 848.
    Tomer SK, Panwar MS (2014) Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. J Stat Comput Simul (to appear)Google Scholar
  33. 857.
    Tse SK, Xiang L (2003) Interval estimation for Weibull-distributed life data under Type II progressive censoring with random removals. J Biopharm Stat 13:1–16CrossRefzbMATHGoogle Scholar
  34. 858.
    Tse SK, Yang C (2003) Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals. J Appl Stat 30:709–718CrossRefzbMATHMathSciNetGoogle Scholar
  35. 859.
    Tse SK, Yuen HK (1998) Expected experiment times for the Weibull distribution under progressive censoring with random removals. J Appl Stat 25:75–83CrossRefzbMATHGoogle Scholar
  36. 860.
    Tse SK, Yang C, Yuen HK (2000) Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. J Appl Stat 27:1033–1043CrossRefzbMATHGoogle Scholar
  37. 905.
    Wu SJ (2003) Estimation for the two-parameter Pareto distribution under progressive censoring with uniform removals. J Stat Comput Simul 73:125–134CrossRefzbMATHMathSciNetGoogle Scholar
  38. 910.
    Wu SJ, Chang CT (2002) Parameter estimations based on exponential progressive type II censored data with binomial removals. Int J Inform Manag Sci 13:37–46zbMATHMathSciNetGoogle Scholar
  39. 916.
    Wu CC, Wu SF, Chan HY (2006b) MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals. Appl Math Comput 181:1657–1670CrossRefzbMATHMathSciNetGoogle Scholar
  40. 919.
    Wu SJ, Chen YJ, Chang CT (2007b) Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution. J Stat Comput Simul 77:19–27CrossRefzbMATHMathSciNetGoogle Scholar
  41. 936.
    Yuen HK, Tse SK (1996) Parameters estimation for Weibull distributed lifetimes under progressive censoring with random removals. J Stat Comput Simul 55:57–71CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • N. Balakrishnan
    • 1
  • Erhard Cramer
    • 2
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Institute of StatisticsRWTH Aachen UniversityAachenGermany

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