Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Type-II stepwise progressive censoring

  • Received : 2015.10.16
  • Accepted : 2016.01.13
  • Published : 2016.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Type-II progressive censoring is one of the censoring methods frequently used in clinical studies, reliability trials, quality control of products and industrial experiments. Sometimes in Type-II progressive censoring experiments, the failure rate is low so the waiting time to observe the $m^{th}$ failure will be very long; however, the experimenter may have to terminate the experiment before a predetermined time. In this article, if two generalized types of Type-II progressive censoring are reminded, we then make some changes in the removal method of Type-II progressive censoring such that without reducing the deduction quality, the termination time of the experiment decreases. This can be done with decreasing withdraws throughout the steps of the experiment with a special reasonable method. A simulation study is done and the results are tabulated at the end of this article for a comparison between introduced method and Type-II progressive censoring.

Keywords

References

  1. Bairamov I and Parsi S (2011). On flexible progressive censoring, Journal of Computational and Applied Mathematics, 235, 4537-4544. https://doi.org/10.1016/j.cam.2010.02.041
  2. Balakrishnan N (2007). Progressive censoring methodology: an appraisal (with discussions), Test, 16, 211-296. https://doi.org/10.1007/s11749-007-0061-y
  3. Balakrishnan N and Aggarwala R (2000). Progressive Censoring: Theory, Methods, and Applications, Birkhauser, Boston.
  4. Balakrishnan N, Burkschat M, Cramer E, and Hofmann G (2008). Fisher information based progres-sive censoring plans, Computational Statistics and Data Analysis, 53, 366-380. https://doi.org/10.1016/j.csda.2008.07.038
  5. Balakrishnan N and Cramer E (2014). The Art of Progressive Censoring, Springer, New York.
  6. Balakrishnan N, Cramer E, and 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, Statistics and Probability Letters, 89, 124-130. https://doi.org/10.1016/j.spl.2014.02.022
  7. Burkschat M (2008). On optimality of extremal schemes in progressive Type-II censoring, Journal of Statistical Planning and Inference, 138, 1647-1659. https://doi.org/10.1016/j.jspi.2007.05.042
  8. Burkschat M, Cramer E, and Kamps U (2006). On optimal schemes in progressive censoring, Statistics and Probability Letters, 76, 1032-1036. https://doi.org/10.1016/j.spl.2005.12.011
  9. Caroni C (2002). The correct ball bearings data, Lifetime Data Anal, 8, 395-399. https://doi.org/10.1023/A:1020523006142
  10. Cohen AC (1963). Progressively censored samples in life testing, Technometrics, 5, 327-329. https://doi.org/10.1080/00401706.1963.10490102
  11. Cramer E (2014). Extreme value analysis for progressively Type-II censored order statistics, Communications in Statistics-Theory and Methods, 43, 2135-2155. https://doi.org/10.1080/03610926.2013.809113
  12. Cramer E and Iliopoulos G (2009). Adaptive progressive Type-II censoring, Test, 19, 342-358.
  13. Cramer E and Kamps U (2001). Estimation with sequential order statistics from exponential distributions, Annals of the Institute of Statistical Mathematics, 53, 307-324. https://doi.org/10.1023/A:1012470706224
  14. Dey S and Dey T (2014). Statistical inference for the Rayleigh distribution under progressively Type-II censoring with binomial removal, Applied Mathematical Modelling, 38, 974-982. https://doi.org/10.1016/j.apm.2013.07.025
  15. Ghitany ME, Al-Jarallah RA, and Balakrishnan N (2013). On the existence and uniqueness of the MLEs of the parameters of a general class of exponentiated distributions, Statistics, 47, 605-612. https://doi.org/10.1080/02331888.2011.614950
  16. Ghitany ME, Tuan VK, and Balakrishnan N (2014). Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data, Journal of Statistical Computation and Simulation, 84, 96-106. https://doi.org/10.1080/00949655.2012.696117
  17. Herd RG (1956). Estimation of parameters of a population from a multi-Censored Sample, Phd Thesis, Iowa State College, Ames, Iowa.
  18. Kamps U and Cramer E (2001). On distributions of generalized order statistics, Statistics, 35, 269-280. https://doi.org/10.1080/02331880108802736
  19. Kang SB and Seo JI (2011). Estimation in an exponentiated half logistic distribution under progres-sively Type-II censoring, Communications for Statistical Applications and Methods, 18, 657-366. https://doi.org/10.5351/CKSS.2011.18.5.657
  20. Kinaci I (2013). A generalization of flexible progressive censoring, Pakistan Journal of Statistics, 29, 377-387.
  21. Krishna H and Kumar K (2013). Reliability estimation in generalized inverted exponential distribution with progressively Type II censored sample, Journal of Statistical Computation and Simulation, 83, 1007-1019. https://doi.org/10.1080/00949655.2011.647027
  22. Lieblein J and ZelenM(1956). Statistical investigation of the fatigue life of deep-groove ball bearings, Journal of Research of the National Bureau of Standards, 57, 273-316. https://doi.org/10.6028/jres.057.033
  23. Ng HKT, Kundu D, and Chan PS (2009). Statistical of analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme, Naval Research logistics, 56, 687-698. https://doi.org/10.1002/nav.20371
  24. Pakyari R and Balakrishnan N (2013). Goodness-of-fit tests for progressively Type-II censored data from location-scale distributions, Journal of Statistical Computation and Simulation, 83, 167-178. https://doi.org/10.1080/00949655.2011.625424
  25. Raqab MZ (2002). Inference for generalized exponential distribution based on record statistics, Journal of Statistical Planning and Inference, 104, 339-350. https://doi.org/10.1016/S0378-3758(01)00246-4
  26. Rezapour M, Alamatsaz MH, and Balakrishnan N (2013a). On properties of dependent progressively Type-II censored order statistics, Metrika, 76, 909-917. https://doi.org/10.1007/s00184-012-0423-7
  27. Rezapour M, Alamatsaz MH, Balakrishnan N, and Cramer E (2013b). On properties of progressively Type-II censored order statistics arising from dependent and nonidentical random variables, Statistical Methodology, 10, 58-71. https://doi.org/10.1016/j.stamet.2012.06.001
  28. Sarhan AM and Al-Ruzaizaa A (2010). Statistical inference in connection with the Weibull model using Type-II progressively censored data with random scheme, Pakistan Journal of Statistics, 26, 267-279.
  29. Seo JI and Kang SB (2014). Predictions for progressively Type-II censored failure times from the half triangle distribution, Communications for Statistical Applications and Methods, 21, 93-103. https://doi.org/10.5351/CSAM.2014.21.1.093
  30. Tse SK, Yang C, and Yuen HK (2000). Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals, Journal of Applied Statistics, 27, 1033-1043. https://doi.org/10.1080/02664760050173355