Computational Statistics

, Volume 32, Issue 4, pp 1665–1687 | Cite as

Prediction of censored exponential lifetimes in a simple step-stress model under progressive Type II censoring

Original Paper
  • 191 Downloads

Abstract

In this article, we consider the problem of predicting survival times of units from the exponential distribution which are censored under a simple step-stress testing experiment. Progressive Type-II censoring are considered for the form of censoring. Two kinds of predictors—the maximum likelihood predictors (MLP) and the conditional median predictors (CMP)—are derived. Some numerical examples are presented to illustrate the prediction methods developed here. Using simulation studies, prediction intervals are generated for these examples. We then compare the MLP and the CMP with respect to mean squared prediction error and the prediction interval.

Keywords

Accelerated testing Conditional median predictor Maximum likelihood predictor Order statistics Mean square prediction error Prediction interval Progressive Type-II censoring 

References

  1. Balakrishnan N (2007) Progressive censoring methodology: an appraisal (with discussions). Test 16:211–296CrossRefMATHMathSciNetGoogle Scholar
  2. Balakrishnan N (2009) A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika 69:351–396CrossRefMATHMathSciNetGoogle Scholar
  3. Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic Press, San DiegoMATHGoogle Scholar
  4. Balakrishnan N, Cramer E (2014) The art of progressive censoring. Birkhauser, BostonCrossRefMATHGoogle Scholar
  5. Balakrishnan N, Han D (2008) Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring. J Stat Plan Inference 138:4172–4186CrossRefMATHMathSciNetGoogle Scholar
  6. Balakrishnan N, Kundu D, Ng HKT, Kannan N (2007) Point and interval estimation for a simple step-stress model with Type-II censoring. J Qual Technol 9:35–47Google Scholar
  7. Bai DS, Kim MS, Lee SH (1989) Optimum simple step-stress accelerated life test with censoring. IEEE Trans Reliab 38:528–532CrossRefMATHGoogle Scholar
  8. Basak P, Balakrishnan N (2003) Maximum likelihood prediction of future record statistics. Ser Qual Reliab Eng Stat Math Stat Methods Reliab 7:159–175CrossRefMathSciNetGoogle Scholar
  9. Basak I, Balakrishnan N (2009) Predictors of failure times of censored items in progressively censored samples from normal distribution. Sankhya Indian J Stat 71–B(part 2):222–249MATHGoogle Scholar
  10. Basak I, Basak P, Balakrishnan N (2006) On some predictors of times to failure of censored items in progressively censored samples. Comput Stat Data Anal 50:1313–1337CrossRefMATHMathSciNetGoogle Scholar
  11. DeGroot MH, Goel PK (1979) Bayesian estimation and optimal design in partially accelerated life testing. Nav Res Logist Q 26:223–235CrossRefMATHMathSciNetGoogle Scholar
  12. Gannoun A, Saracco J, Yu K (2003) Nonparametric prediction by conditional median and quantiles. J Stat Plan Inference 117:207–223CrossRefMATHMathSciNetGoogle Scholar
  13. Gouno E, Balakrishnan N (2001) Step-stress accelerated life test. In: Balakrishnan N, Rao CR (eds) Handbook of statistics—advances in reliability, vol 20. North-Holland, Amsterdam, pp 623–639Google Scholar
  14. Gouno E, Sen A, Balakrishnan N (2004) Optimal step-stress test under progressive Type-I censoring. IEEE Trans Reliab 53:383–393CrossRefGoogle Scholar
  15. Han N, Balakrishnan N, Sen A, Gouno E (2006) Corrections on optimal step-stress test under progressive Type-I censoring. IEEE Trans Reliab 55:613–614CrossRefGoogle Scholar
  16. Kaminsky KS, Nelson PI (1998) Prediction of order statistics. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, 17—order statistics: applications. North-Holland, Amsterdam, pp 431–450CrossRefGoogle Scholar
  17. Kaminsky KS, Rhodin LS (1985) Maximum likelihood prediction. Ann Inst Stat Math 37:707–717CrossRefMATHMathSciNetGoogle Scholar
  18. Kateri M, Balakrishnan N (2008) Inference for a simple step-stress model with Type-II censoring and Weibull distributed lifetimes. IEEE Trans Reliab 57:616–626CrossRefGoogle Scholar
  19. Khamis IH, Higgins JJ (1998) A new model for step-stress testing. IEEE Trans Reliab 47:131–134CrossRefGoogle Scholar
  20. Lee J, Elmore R, Kennedy C, Gray M, Jones W (2011) Lifetime prediction for degradation of solar mirrors under step-stress accelerated testing. In: 2011 workshop on accelerated stress testing and reliabilityGoogle Scholar
  21. Miller R, Nelson WB (1983) Optimum simple step-stress plans for accelerated life testing. IEEE Trans Reliab 32:59–65CrossRefMATHGoogle Scholar
  22. Nelson W (1982) Applied life data analysis. Wiley, New YorkCrossRefMATHGoogle Scholar
  23. Raqab MZ (1997) Modified maximum likelihood predictors of future order statistics from normal samples. Comput Stat Data Anal 25:91–106CrossRefMATHMathSciNetGoogle Scholar
  24. Raqab MZ (2004) Approximate maximum likelihood predictors of future failure times of shifted exponential distribution under multiple type-II censoring. Stat Methods Appl 13:43–54CrossRefMATHMathSciNetGoogle Scholar
  25. Raqab MZ, Nagaraja HN (1995) On some predictors of future order statistics. IMetron LIII–N.1–2:185–204MATHMathSciNetGoogle Scholar
  26. Raqab MZ, Ahmadi J, Arabli BA (2013) Comparisons among some predictors of exponential distributions using pitman closeness. Comput Stat 28:2349–2356CrossRefMATHMathSciNetGoogle Scholar
  27. Tang LC (2003) Multiple steps step-stress accelerated tests. In: Pham H (ed) Handbook of reliability engineering. Springer, New York, pp 441–455CrossRefGoogle Scholar
  28. Xiong C (1998) Inference on a simple step-stress model with Type-II censored exponential data. IEEE Trans Reliab 47:142–146CrossRefGoogle Scholar
  29. Xiong C, Ji M (2004) Analysis of grouped and censored data from step-stress life test. IEEE Trans Reliab 52:22–28CrossRefGoogle Scholar
  30. Xiong C, Milliken GA (2002) Prediction for exponential lifetimes based on step-stress testing. Commun Stat Simul Comput 31:539–556CrossRefMATHMathSciNetGoogle Scholar
  31. Yang C-H, Tong L-I (2006) Predicting Type-II censored data from factorial experiments using modified maximum likelihood predictor. Int J Adv Manuf Technol 30:887–896CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Penn State AltoonaAltoonaUSA
  2. 2.McMaster UniversityHamiltonCanada

Personalised recommendations