BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks

Fallah A, Asgharzadeh A, Ng H K T. Prediction Based on Type-II Censored Coherent System Lifetime Data under a Proportional Reversed Hazard Rate Model. JIRSS. 2021; 20 (1) :153-181

URL: http://jirss.irstat.ir/article-1-780-en.html

URL: http://jirss.irstat.ir/article-1-780-en.html

In this paper, we discuss the prediction problem based on censored coherent system lifetime data when the system structure is known and the component lifetime follows the proportional reversed hazard model. Different point and interval predictors based on classical and Bayesian approaches are derived. A numerical example is presented to illustrate the prediction methods used in this paper. Monte Carlo simulation study is performed to evaluate and compare the performances of different prediction methods.

Type of Study: Original Paper |
Subject:
62Nxx: Survival analysis and censored data

Received: 2020/07/23 | Accepted: 2020/12/23 | Published: 2021/06/20

Received: 2020/07/23 | Accepted: 2020/12/23 | Published: 2021/06/20

1. Asgharzadeh, A. Fallah, A., Raqab, M. Z. and Valiollahi, R. (2018), Statistical inference based on Lindley record data. Statistical Papers, 59, 759-779. [DOI:10.1007/s00362-016-0788-1]

2. Asgharzadeh, A., Valiollahi, R. and Kundu, D. (2015), Prediction for future failures in Weibull distribution under hybrid censoring. Journal of Statistical Computation and Simulation, 85, 824-838. [DOI:10.1080/00949655.2013.848451]

3. Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011a), Linear inference for Type-II censored lifetime data of reliability systems with known signatures. IEEE Transactions on Reliability, 60, 426--440.

4. Balakrishnan, N., Ng, H. K. T., and Navarro, J. (2011b), Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures. Journal of Nonparametric Statistics, 23, 741-752.

5. Bhattacharya and Samaniego (2010), Estimating component characteristics from system failure time data. Naval Research Logistics, 57, 380-389. [DOI:10.1002/nav.20407]

6. Basak, I., Basak, P., and Balakrishnan, N. (2006), On some predictors of times to failures of censored items in progressively censored sample. Computational Statistics and Data Analysis, 50, 1313-1337. [DOI:10.1016/j.csda.2005.01.011]

7. Basak, I., and N. Balakrishnan, N. (2017), Prediction of censored exponential lifetimes in a simple step-stress model under progressive Type II censoring. Computational Statistics, 32, 1665-1687. [DOI:10.1007/s00180-016-0684-0]

8. Chahkandi, M., Ahmadi, J., and Baratpour, S. (2014), Non-parametric prediction intervals for the lifetime of coherent systems. Statistical Papers, 55, 1019-1034. [DOI:10.1007/s00362-013-0549-3]

9. Chivers, C. (2012), MH adaptive: General Markov Chain Monte Carlo for Bayesian Inference using adaptive Metropolis-Hastings sampling, R package.

10. Kaminsky, K. S., and Rhodin, L. S. (1985), Maximum likelihood prediction. Annals of the Institute of Statistical Mathematics, 37, 507-517. [DOI:10.1007/BF02481119]

11. Kochar, S., Mukerjee, H., and Samaniego, F. J. (1999), The Signature of a Coherent System and its Application to Comparisons Among Systems. Naval Research Logistics, 46, 507-523.
https://doi.org/10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D [DOI:10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-D]

12. Navarro, J., and R. Rubio, R. (2010), Computations of coherent systems with five components. Communications in Statistics -- Simulation and Computation, 39, 68-84. [DOI:10.1080/03610910903312185]

13. Navarro, J., Ruiz, J. M., and Sandoval, C. J. (2007), Properties of coherent systems with dependent components, Communications in Statistics - Theory and Methods, 36, 175-191.

14. Navarro, J., Samaniego, F. J., Balakrishnan, N., and Bhattacharya, D. (2008), On the application and extension of system signatures in engineering reliability. Naval Research Logistics, 55, 313-327. [DOI:10.1002/nav.20285]

15. Ng, H. K. T., Navarro, J., and Balakrishnan, N. (2012), Parametric inference from system lifetime data under a proportional hazard rate model. Metrika, 75, 367-388. [DOI:10.1007/s00184-010-0331-7]

16. Raqab, M. Z., and Nagaraja, H. N. (1995), On some predictors of future order statistics. Metron, 53, 185-204.

17. Raqab, M. Z., Alkhalfan, L. A., Bdair, O. M., and Balakrishnan, N. (2019), Maximum likelihood prediction of records from 3-parameter Weibull distribution and some approximations. Journal of Computational and Applied Mathematics, 356, 118-132. [DOI:10.1016/j.cam.2019.02.006]

18. R Core Team (2019), R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.

19. Robert, C., and Casella, G. (2004), Monte Carlo Statistical Methods, 2nd edition. New York: Springer.

20. Saadati Nik, A., Asgharzadeh, A., and Raqab, M. Z. (2020), Prediction Methods for Future Failure Times Based on Type-II Right-Censored Samples from New Pareto-Type Distribution. Journal of Statistical Theory and Practice, 14, 39. [DOI:10.1007/s42519-020-00106-7]

21. Samaniego, F. J. (1985), On closure of the IFR class under formation of coherent systems. IEEE Transactions on Reliability Theory, 34, 69-72. [DOI:10.1109/TR.1985.5221935]

22. Samaniego, F. J. (2007), System Signatures and their Applications in Engineering Reliability, International Series in Operations Research and Management Science 110. Springer, New York.

23. Yang, Y., Ng, H. K. T., and Balakrishnan, N. (2016), A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature, Computational Statistics, 31, 609-641.

24. Yang, Y., Ng, H. K. T., and Balakrishnan, N. (2019), Expectation maximization algorithm for system based lifetime data with unknown system structure. AStA Advanced Statistical Analysis, 103, 69-98. [DOI:10.1007/s10182-018-0323-x]

25. Zhang, J., Ng, H. K. T., and Balakrishnan, N. (2015a), Statistical inference of component lifetimes with location-scale distributions from censored system failure data with known signature. IEEE Transactions on Reliability, 64, 613-626.

26. Zhang, J., Ng, H. K. T., and Balakrishnan, N. (2015b), Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures. Naval Research Logistics, 62, 550-563.

Send email to the article author

Rights and permissions | |

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |