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Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

  • El-Dina, M.M. Mohie (Department of Mathematics, Faculty of Science, Al-Azhar University) ;
  • Abu-Youssef, S.E. (Department of Mathematics, Faculty of Science, Al-Azhar University) ;
  • Ali, Nahed S.A. (Department of Mathematics, Faculty of Education, Ain Shams University) ;
  • Abd El-Raheem, A.M. (Department of Mathematics, Faculty of Education, Ain Shams University)
  • Received : 2016.06.25
  • Accepted : 2016.07.08
  • Published : 2016.07.31

Abstract

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

Keywords

References

  1. Ahmadi J, Jozani MJ, Marchand E, and Parsian A (2009). Bayes estimation based on k-record data from a general class of distributions under balanced type loss functions, Journal of Statistical Planning and Inference, 139, 1180-1189 https://doi.org/10.1016/j.jspi.2008.07.008
  2. Bai DS, Kim MS, and Lee SH (1989). Optimum simple step-stress accelerated life tests with censoring, IEEE Transactions on Reliability, 38, 528-532. https://doi.org/10.1109/24.46476
  3. Balakrishnan N and Aggarwala R (2000). Progressive Censoring: Theory, Methods, and Applications, Birkhauser, Boston.
  4. Balakrishnan N and Cramer E (2014). The Art of Progressive Censoring: Applications to Reliability and Quality, Birkhauser, New York.
  5. Balakrishnan N, Kundu D, Ng HKT, and Kannan N (2007). Point and interval estimation for a simple step-stress model with type-II censoring, Journal of Quality Technology, 39, 35-47. https://doi.org/10.1080/00224065.2007.11917671
  6. Efron B and Tibshirani RJ (1993). An Introduction to the Bootstrap, Chapman & Hall, London.
  7. Gouno E, Sen A, and Balakrishnan N (2004). Optimal step-stress test under progressive type-I censoring, IEEE Transactions on Reliability, 53, 388-393. https://doi.org/10.1109/TR.2004.833320
  8. Ismail AA (2012). Estimating the parameters of Weibull distribution and the acceleration factor from hybrid partially accelerated life test, Applied Mathematical Modelling, 36, 2920-2925. https://doi.org/10.1016/j.apm.2011.09.083
  9. Ismail AA (2014). Inference for a step-stress partially accelerated life test model with an adaptive type-II progressively hybrid censored data from Weibull distribution, Journal of Computational and Applied Mathematics, 260, 533-542. https://doi.org/10.1016/j.cam.2013.10.014
  10. Kim C, Jung J, and Chung Y (2011). Bayesian estimation for the generalized Weibull model under type II progressive censoring, Statistical Papers, 52, 53-70. https://doi.org/10.1007/s00362-009-0203-2
  11. Miller R (1981). Survival Analysis, Wiley, New York.
  12. Miller R and Nelson W (1983). Optimum simple step-stress plans for accelerated life testing, IEEE Transactions on Reliability, 32, 59-65.
  13. Mohie El-Din MM, Abu-Youssef SE, Ali NSA, and Abd El-Raheem AM (2015a). Estimation in step-stress accelerated life tests for Weibull distribution with progressive first-failure censoring, Journal of Statistics Applications & Probability, 3, 403-411.
  14. Mohie El-Din MM, Abu-Youssef SE, Ali NSA, and Abd El-Raheem AM (2015b). Estimation in step-stress accelerated life tests for power generalized Weibull distribution with progressive censoring, Advances in Statistics, 2015, 1-13.
  15. Mohie El-Din MM, Abu-Youssef SE, Ali NSA, and Abd El-Raheem AM (2016). Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring, Metron, 7, 1-21.
  16. Nadarajah S and Haghighi F (2011). An extension of the exponential distribution, Statistics, 45, 543-558. https://doi.org/10.1080/02331881003678678
  17. Nassar MM and Eissa FH (2005). Bayesian estimation for the exponentiated Weibull model, Communications in Statistics - Theory and Methods, 33, 2343-2362. https://doi.org/10.1081/STA-200031447
  18. Nelson W (1990). Accelerated Testing: Statistical Models, Test Plans and Data Analysis,Wiley, New York.
  19. Pakyari R and Balakrishnan N (2012). A general purpose approximate goodness-of-fit test for progressively type-II censored data, IEEE Transactions on Reliability, 61, 238-244. https://doi.org/10.1109/TR.2012.2182811
  20. Singh SK, Singh U, Kumar M, and Vishwakarma PK (2014a). Classical and Bayesian inference for an extension of the exponential distribution under progressive type-II censored data with binomial removals, Journal of Statistics Applications & Probability Letters, 1, 75-86. https://doi.org/10.12785/jsapl/010304
  21. Singh SK, Singh U, and Sharma VK (2014b). Bayesian estimation and prediction for the generalized Lindley distribution under asymmetric loss function, Hacettepe Journal of Mathematics and Statistics, 43, 661-678.
  22. Srivastava PW and Shukla R (2008a). A log-logistic step-stress model, IEEE Transactions on Reliability, 57, 431-434. https://doi.org/10.1109/TR.2008.928182
  23. Srivastava PW and Shukla R (2008b). Optimum log-logistic step-stress model with censoring, International Journal of Quality & Reliability Management, 25, 968-976. https://doi.org/10.1108/02656710810908115
  24. Srivastava PW and Mittal N (2010). Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring, Applied Mathematical Modelling, 34, 3166-3178. https://doi.org/10.1016/j.apm.2010.02.007
  25. Upadhyay SK and Gupta A (2010). A Bayes analysis of modified Weibull distribution via Markov chain Monte Carlo simulation, Journal of Statistical Computation and Simulation, 80, 241-254. https://doi.org/10.1080/00949650802600730
  26. Zhu Y (2010). Optimal design and equivalency of accelerated life testing plans (Doctoral dissertation), Rutgers University, New Brunswick, NJ.