Exact inference for a simple step-stress model with Type-I hybrid censored data from the exponential distribution

Journal of Statistical Planning and Inference

Volumn 137, Issue 11, 2007, Pages 3268-3290

  Balakrishnan, N ^a   Xie, Qihao ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Accelerated testing; Bootstrap method; Conditional moment generating function; Coverage probability; Cumulative exposure model; Exponential distribution; Maximum likelihood estimation; Order statistics; Step stress models; Tail probability; Type I hybrid censoring; Type II hybrid censoring

Indexed keywords

EID: 34447505961     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.03.011     Document Type: Article

References (37)

1. Arnold B.C., Balakrishnan N., and Nagaraja H.N. A First Course in Order Statistics (1992), Wiley, New York
2. Bagdonavicius V., and Nikulin M. Accelerated Life Models: Modeling and Statistical Analysis (2002), Chapman & Hall/CRC Press, Boca Raton, FL
3. Bai D.S., Kim M.S., and Lee S.H. Optimum simple step-stress accelerated life test with censoring. IEEE Trans. Reliab. 38 (1989) 528-532
4. Balakrishnan N., Kundu D., Ng H.K.T., and Kannan N. Point and interval estimation for a simple step-stress model with Type-II censoring. J. Qual. Technol. 39 (2007) 35-47
5. Barlow R.E., Madansky A., Proschan F., and Scheuer E. Statistical estimation procedure for the "burn-in" process. Technometrics 10 (1968) 51-62
6. Bartholomew D.J. The sampling distribution of an estimate arising in life testing. Technometrics 5 (1963) 361-374
7. Bhattacharyya G.K., and Zanzawi S. A tampered failure rate model for step-stress accelerated life test. Comm. Statist. Theory and Methods 18 (1989) 1627-1643
8. Chandrasekar B., Childs A., and Balakrishnan N. Exact likelihood inference for the exponential distribution under general Type-I and Type-II hybrid censoring. Naval Res. Logist. 51 (2004) 994-1004
9. Chen S.M., and Bhattacharyya G.K. Exact confidence bound for an exponential parameter under hybrid censoring. Comm. Statist. Theory Methods 17 (1988) 1858-1870
10. Childs A., Chandrasekar B., Balakrishnan N., and Kundu D. Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann. Inst. Statist. Math. 55 (2003) 319-330
11. David H.A., and Nagaraja H.N. Order Statistics. third ed. (2003), Wiley, Hoboken, NJ
12. DeGroot M.H., and Goel P.K. Bayesian estimation and optimal design in partially accelerated life testing. Naval Res. Logist. Quart. 26 (1979) 223-235
13. Ebrahimi N. Estimating the parameter of an exponential distribution from hybrid life test. J. Statist. Plann. Inference 14 (1986) 255-261
14. Ebrahimi N. Prediction intervals for future failures in the exponential distribution under hybrid censoring. IEEE Trans. Reliab. 41 (1992) 127-132
15. Efron B. The Jackknife, the Booststrap and Other Re-sampling Plans, CBMS/NSF Regional Conference Series in Applied Mathematics vol. 38 (1982), SIAM, Philadelphia, PA
16. Epstein B. Truncated life tests in the exponential case. Ann. Math. Statist. 25 (1954) 555-564
17. Fairbanks K., Madson R., and Dykstra R. A confidence interval for an exponential parameter from a hybrid life test. J. Amer. Statist. Assoc. 77 (1982) 137-140
18. Gouno E., and Balakrishnan N. Step-stress accelerated life test. In: Balakrishnan N., and Rao C.R. (Eds). Handbook of Statistics-20. Advances in Reliability (2001), North-Holland, Amsterdam 623-639
19. Gouno E., Sen A., and Balakrishnan N. Optimal step-stress test under progressive Type-I censoring. IEEE Trans. Reliab. 53 (2004) 383-393
20. Gupta R.D., and Kundu D. Hybrid censoring with exponential failure distributions. Comm. Statist. Theory Methods 27 (1998) 3065-3083
21. Hall P. Theoretical comparison of bootstrap confidence intervals. Ann. Statist. 16 (1988) 927-953
22. Hanagal D.D. Inference procedures in some bivariate exponential models under hybrid random censoring. Statist. Papers 38 (1997) 169-189
23. Jeong H.S., Park J.I., and Yum B.J. Development of (r, T) hybrid sampling plans for exponential lifetime distributions. J. Appl. Statist. 23 (1996) 601-607
24. Johnson, N.L., Kotz, S., Balakrishnan, N., 1994. Continuous Univariate Distributions, vol. 2, second ed. Wiley, New York.
25. Khamis I.H., and Higgins J.J. A new model for step-stress testing. IEEE Trans. Reliab. 47 (1998) 131-134
26. Kundu D., and Basu S. Analysis of incomplete data in presence of competing risks. J. Statist. Plann. Inference 87 (2000) 221-239
27. Madi M.T. Multiple step-stress accelerated life test: the tampered failure rate model. Comm. Statist. Theory Methods 22 (1993) 2631-2639
28. Meeker W.Q., and Escobar L.A. Statistical Methods for Reliability Data (1998), Wiley, New York
29. MIL-STD-781 C, 1977. Reliability Design Qualification and Production Acceptance Test, Exponential Distribution. U.S. Government Printing Office, Washington, D.C.
30. Miller R., and Nelson W.B. Optimum simple step-stress plans for accelerated life testing. IEEE Trans. Reliab. 32 (1983) 59-65
31. Nelson W. Accelerated life testing: step-stress models and data analysis. IEEE Trans. Reliab. 29 (1980) 103-108
32. Nelson W. Accelerated Testing: Statistical Models, Test Plans, and Data Analyses (1990), Wiley, New York
33. Tang L.C. Multiple steps step-stress accelerated tests. In: Pham H. (Ed). Handbook of Reliability Engineering (2003), Springer, New York 441-455 (Chapter 24)
34. Watkins A.J. Commentary: inference in simple step-stress models. IEEE Trans. Reliab. 50 (2001) 36-37
35. Xiong C. Inference on a simple step-stress model with Type-II censored exponential data. IEEE Trans. Reliab. 47 (1998) 142-146
36. Xiong C., and Ji M. Analysis of grouped and censored data from step-stress life test. IEEE Trans. Reliab. 53 (2004) 22-28
37. Xiong C., and Milliken G.A. Step-stress life-testing with random stress change times for exponential data. IEEE Trans. Reliab. 48 (1999) 141-148