Volume 20, Issue 1 (6-2021)                   JIRSS 2021, 20(1): 123-152 | Back to browse issues page


XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Cramer E, Laumen B. Stage Life Testing with Missing Stage Information - an EM-Algorithm Approach. JIRSS. 2021; 20 (1) :123-152
URL: http://jirss.irstat.ir/article-1-779-en.html
Institute of Statistics, RWTH Aachen University, D-52062 Aachen, GERMANY , erhard.cramer@rwth-aachen.de
Abstract:   (212 Views)

We consider a stage life testing model and assume that the information at which levels the failures occurred is not available. In order to find estimates for the lifetime distribution parameters, we propose an EM-algorithm approach which interprets the lack of knowledge about the stages as missing information. Furthermore, we illustrate the implementation difficulties caused by an increasing number of stages. The study is supplemented by a data example as well as simulations.

Full-Text [PDF 235 kb]   (140 Downloads)    
Type of Study: Original Paper | Subject: 62Fxx: Parametric inference
Received: 2020/11/23 | Accepted: 2021/02/7 | Published: 2021/06/20

References
1. Atkinson, K. E. (1989). An introduction to numerical analysis, John Wiley & Sons, Inc., 2nd edition.
2. Bairamov, I., and Eryilmaz, S. (2006). Spacings, exceedances and concomitants in progressive Type II censoring scheme. J. Statist. Plann. Inference, 136(3), 527-536. [DOI:10.1016/j.jspi.2004.09.002]
3. Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika, 69, 351-396. [DOI:10.1007/s00184-008-0221-4]
4. Balakrishnan, N., and Aggarwala, R. (2000). Progressive censoring: theory, methods, and applications. Birkhauser, Boston.
5. Balakrishnan, N., and Cramer, E. (2014). The Art of Progressive Censoring: Applications to Reliability and Quality. Statistics for Industry and Technology. Birkhauser, New York.
6. Balakrishnan, N., and Cramer, E. (2021). Progressive censoring methodology: A review. In Pham, H., editor, Springer Handbook of Engineering Statistics, Springer, New York, 2. edition, to appear.
7. Balakrishnan, N., Han, D., and Iliopoulos, G. (2011). Exact inference for progressively Type-I censored exponential failure data. Metrika, 73(3), 335-358. [DOI:10.1007/s00184-009-0281-0]
8. Balakrishnan, N., and Kateri, M. (2008). On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data.
9. Statistics & Probability Letters, 78(17), 2971-2975.
10. Cramer, E. (2017). Progressive Censoring Schemes. Inem Wiley StatsRef: Statistics Reference Online, Hoboken, NJ. John Wiley & Sons, Ltd.
11. David, H. A., and Nagaraja, H. N. (1998). Concomitants of order statistics. In Balakrishnan, N. and Rao, C. R., editors, Handbook of Statistics: Order Statistics: Theory & Methods, 16, 487-513. Elsevier, Amsterdam. [DOI:10.1016/S0169-7161(98)16020-0]
13. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B(Methodological), 39(1), 1-38. [DOI:10.1111/j.2517-6161.1977.tb01600.x]
14. Henningsen, A., and Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443-458. [DOI:10.1007/s00180-010-0217-1]
15. Izadi, M., and Khaledi, B.-E. (2007). Progressive {Type II censored order statistics and their concomitants: some stochastic comparisons results. J. Iran. Stat. Soc. (JIRSS), 6, 111-124.
16. Kundu, D., and Ganguly, A. (2017). Analysis of Step-Stress Models. Academic Press Inc., London, UK.
17. Laumen, B. (2017). Progressive Censoring and Stage Life Testing. PhD thesis, RWTH Aachen University.
18. Laumen, B., and Cramer, E. (2019a). Progressive censoring with fixed censoring times. Statistics, 53, 569-600.
19. Laumen, B., and Cramer, E. (2019b). Stage life testing. Nav. Res. Logistics, 53, 632-647.
20. Laumen, B., and Cramer, E. (2021a). k-step stage life testing. Statist. Neerlandica, 75, 203-223.
21. Laumen, B., and Cramer, E. (2021b). Stage life testing with random stage changing times. Commun. Statist. Theory Meth., DOI:10.1080/03610926.2020.1805764, to appear. [DOI:10.1080/03610926.2020.1805764]

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2015 All Rights Reserved | Journal of The Iranian Statistical Society