On estimation of modified Weibull parameters in presence of accelerated life test

References

• Bai, D. S., and S. W. Chung. 1992. Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring. IEEE Transactions on Reliability 41 (3):400–6. doi:10.1109/24.159807.
   Web of Science ®Google Scholar
• Balakrishnan, N. 2007. Progressive censoring methodology: An appraisal (with discussions). Test 16:211–26. doi:10.1007/s11749-007-0061-y.
   Web of Science ®Google Scholar
• Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring: Theory, methods and applications. Boston, MA: Birkhäuser.
   Google Scholar
• Balakrishnan, N., and R. A. Sandhu. 1995. A simple simulation algorithm for generating progressively type-II censored samples. American Statistician 49:229–30.
   Web of Science ®Google Scholar
• Barlow, R. E., and F. Proschan. 1981. Statistical theory of reliability and life testing. Silver Spring, MD.
   Google Scholar
• Bhattacharyya, G. K., and Z. A. Soejoeti. 1989. Tampered failure rate model for step-stress accelerated life test. Communications in Statistics - Theory and Methods 18:1627–1643. doi:10.1080/03610928908829990.
   Web of Science ®Google Scholar
• Cohen, A. C. 1965. Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics 7:579–88. doi:10.1080/00401706.1965.10490300.
   Web of Science ®Google Scholar
• Efron, B. 1982. The bootstrap and other resampling plans. Philadelphia, PA: SIAM.
   Google Scholar
• EL-Sagheer, R. M. 2016a. Estimation of parameters of Weibull-gamma distribution based on progressively censored data. Statistical Papers July. doi:10.1007/s00362-016-0787-2.
   PubMed Web of Science ®Google Scholar
• EL-Sagheer, R. M. 2016b. Inferences in constant-partially accelerated life tests based on progressive type-II censoring. Bulletin of the Malaysian Mathematical Sciences Society February. doi:10.1007/s40840-016-0311-9.
   Web of Science ®Google Scholar
• EL-Sagheer, R. M., and M. Ahsanullah. 2015. Statistical inference for a step-stress partially accelerated life test model based on progressively type-II censored data from Lomax distribution. Journal of Applied Statistical Science 21 (4):307–23.
   Google Scholar
• Fan, T. H., W. L. Wang, and N. Balakrishnan. 2008. Exponential progressive step-stress life-testing with link function based on Box Cox transformation. Journal of Statistical Planning and Inference 138:2340–54. doi:10.1016/j.jspi.2007.10.002.
   Web of Science ®Google Scholar
• Gasmi, S., and M. Berzig. 2011. Parameters estimation of the modified Weibull distribution based on type-I censored samples. Applied Mathematical Sciences 5:2899–917.
   Google Scholar
• Gelfand, A. E., S. E. Hills, A. Racine-Poon, and A. F. M. Smith. 1990. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association 85:972–85. doi:10.1080/01621459.1990.10474968.
   Web of Science ®Google Scholar
• Gelfand, A. E., and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85:398–409. doi:10.1080/01621459.1990.10476213.
   Web of Science ®Google Scholar
• Geman, S., and D. Geman. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Transactions on Pattern Analysis and Machine Intelligence 6:721–41. doi:10.1109/TPAMI.1984.4767596.
   PubMed Web of Science ®Google Scholar
• Gouno, E., A. Sen, and N. Balakrishnan. 2004. Optimal step-stress test under progressive Type-I censoring. IEEE Transactions on Reliability 53:388–93. doi:10.1109/TR.2004.833320.
   Web of Science ®Google Scholar
• Hall, P. 1988. Theoretical comparison of bootstrap confidence intervals. Annals of Statistics 16:927–53. doi:10.1214/aos/1176350933.
   Web of Science ®Google Scholar
• Hassan, A. S., and A. S. Al-Ghamdi. 2009. Optimum step stress accelerated life testing for Lomax distribution. Journal of Applied Sciences Research 5:2153–64.
   Google Scholar
• Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109. doi:10.1093/biomet/57.1.97.
   Web of Science ®Google Scholar
• Ismail, A. A. 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 260:533–42. doi:10.1016/j.cam.2013.10.014.
   Web of Science ®Google Scholar
• Ismail, A. A., A. A. Abdel-Ghalyb, and E. H. El-Khodary. 2011. Optimum constant-stress life test plans for Pareto distribution under type-I censoring. Journal of Statistical Computation and Simulation 81 (12):1835–45. doi:10.1080/00949655.2010.506440.
   Web of Science ®Google Scholar
• Ismail, A. A., and H. M. Aly. 2010. Optimal planning of failure-step stress partially accelerated life tests under type-II censoring. Journal of Statistical Computation and Simulation 80 (12):1335–48. doi:10.1080/00949650903071096.
   Web of Science ®Google Scholar
• Lawless, J. F. 2003. Statistical models and methods for lifetime data. New York, NY: John Wiley and Sons.
   Google Scholar
• Madi, M. T., and M. Z. Raqab. 2009. Bayesian inference for the generalized exponential distribution based on progressively censored data. Communications in Statistics-Theory and Methods 38:2016–29. doi:10.1080/03610920902855951.
   Web of Science ®Google Scholar
• Mahmoud, M. A. W., R. M. EL-Sagheer, A. A. Soliman, and A. H. Abd-Ellah. 2014. Inferences of the lifetime performance index with Lomax distribution based on progressive type-II censored. Economic Quality Control 29:39–51. doi:10.1515/eqc-2014-0005.
   Google Scholar
• Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equations of state calculations by fast computing machines. Journal of Chemical Physics 21:1087–91. doi:10.1063/1.1699114.
   Web of Science ®Google Scholar
• Musleh, R. M., and A. Helu. 2014. Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study. Reliability Engineering and System Safety 131:216–27. doi:10.1016/j.ress.2014.07.006.
   Web of Science ®Google Scholar
• Nelson, W. 1990. Accelerated testing: Statistical models, test plans and data analysis. New York, NY: Wiley.
   Google Scholar
• Rao, B. R. 1992. Equivalence of the tampered random variable and the tampered failure rate models in accelerated life testing for a class of life distributions. Communications in Statistics-Theory and Methods 21:647–64. doi:10.1080/03610929208830805.
   Web of Science ®Google Scholar
• Sarhan, A. M., and M. Zaindin. 2009. Modified Weibull distribution. Applied Sciences 11:123–36.
   Google Scholar
• Soliman, A. A., A. H. Abd-Ellah, N. A. Abou-Elheggag, and R. M. EL-Sagheer. 2015. Inferences using type-II progressively censored data with binomial removals. Arabian Journal of Mathematics 4 (2):127–39. doi:10.1007/s40065-015-0127-8.
   Web of Science ®Google Scholar
• Tangi, Y., Q. Guani, P. Xu, and H. Xu. 2012. Optimum design for type-I step-stress accelerated life tests of two-parameter Weibull distributions. Communications in Statistics-Theory and Methods 41:3863–77. doi:10.1080/03610926.2012.707456.
   Web of Science ®Google Scholar
• Tierney, L. 1994. Markov chains for exploring posterior distributions. Annals of Statistics 22:1701–28. doi:10.1214/aos/1176325750.
   Web of Science ®Google Scholar
• Wu, S. J., Y. P. Lin, and S. T. Chen. 2008. Optimal step-stress test under type I progressive group-censoring with random removals. Journal of Statistical Planning and Inference 138:817–26. doi:10.1016/j.jspi.2007.02.004.
   Web of Science ®Google Scholar
• Zaindin, M. 2010. Parameter estimation of the modified Weibull model based on grouped and censored data. International Journal of Basic and Applied Sciences 10 (2):122–32.
   Google Scholar