Selection of the best minimal repair systems for Weibull lifetime distribution: A Bayesian approach

References

• Amini, M., and N. Balakrishnan. 2013. Nonparametric Meta-analysis of independent samples of records. Computational Statistics and Data Analysis 66 :70–81. doi:10.1016/j.csda.2013.03.019.
   Web of Science ®Google Scholar
• Amini, M., and N. Balakrishnan. 2015. Pooled parametric inference for minimal repair systems. Computational Statistics 30 (2):605–23. doi:10.1007/s00180-014-0552-8.
   Web of Science ®Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1998. Records. New York: John Wiley & Sons.
   Google Scholar
• Balakrishnan, N., N. Kannan, and H. N. Nagaraja. 2007. Advances in ranking and selection, Multiple comparisons and reliability: Methodology and applications. USA: Springer Science & Business Media.
   Google Scholar
• Bain, L., and M. Engelhardt. 1991. Statistical theory of reliability and Life-Testing models. New York: Marcel-Dekker.
   Google Scholar
• Balakrishnan, N., H. K. T. Ng, and S. Panchapakesan. 2006. A nonparametric procedure based on early failures for selecting the best population using a test for equality. Journal of Statistical Planning and Inference 136 (7):2087–111. doi:10.1016/j.jspi.2005.08.034.
   Web of Science ®Google Scholar
• Barlow, R. E., and L. C. Hunter. 1960. Optimum preventive maintenance policies. Operations Research 8 (1):90–100. doi:10.1287/opre.8.1.90.
   Web of Science ®Google Scholar
• Bechhofer, R. G. R. E. 1995. Design and analysis of experiment for statistical selection, screening, and multiple comparisons (No. 04; QA279, B4.).
   Google Scholar
• Boesel, J., B. L. Nelson, and S. H. Kim. 2003. Using ranking and selection to “clean up” after simulation optimization. Operations Research 51 (5):814–25. doi:10.1287/opre.51.5.814.16751.
   Web of Science ®Google Scholar
• Calabria, R., and G. Pulcini. 1994. An engineering approach to Bayes estimation for the weibull distribution. Microelectronics Reliability 34 (5):789–802. doi:10.1016/0026-2714(94)90004-3.
   Web of Science ®Google Scholar
• Canavos, G. C., and C. P. Taokas. 1973. Bayesian estimation of life parameters in the Weibull distribution. Operations Research 21 (3):755–63. doi:10.1287/opre.21.3.755.
   Web of Science ®Google Scholar
• Dailami, N., M. B. Rao, and K. Subramanyam. 1985. On the Selection of the Best Gamma Population. Determination of minimax sample sizes (No. TR-85-42). Pittsburgh Univ PA Center for Multivariate Analysis.
   Google Scholar
• Dudewicz, E. J. 1980. Ranking (ordering) and selection: An overview of how to select the best. Technometrics 22 (1):113–9. doi:10.2307/1268390.
   Web of Science ®Google Scholar
• Gaver, D. P., and I. G. O'Muircheartaigh. 1987. Robust empirical Bayes analysis of event rates. Technometrics 29 (1):1–15. doi:10.1080/00401706.1987.10488178.
   Web of Science ®Google Scholar
• Geertsema, J. C. 1972. Nonparametric sequential procedures for selecting the best of k populations. Journal of the American Statistical Association 67 (339):614–6. doi:10.2307/2284450.
   Web of Science ®Google Scholar
• Follmann, D. A., and M. S. Goldberg. 1988. Distinguishing heterogeneity from decreasing hazard rates. Technometrics 30 (4):389–96. doi:10.1080/00401706.1988.10488433.
   Web of Science ®Google Scholar
• Goel, P. K., and H. Rubin. 1977. On selecting a subset containing the best population: a bayesian approach. The Annals of Statistics 5 (5):969–83. doi:10.1214/aos/1176343952.
   Web of Science ®Google Scholar
• Golparvar, L., and A. Parsian. 2017. Selecting the best exponential population under Type-II progressive censoring scheme via empirical Bayes approach. Communications in Statistics-Simulation and Computation 46 (1):404–22. doi:10.1080/03610918.2014.964806.
   Web of Science ®Google Scholar
• Green, E. J., F. A. Roesch, Jr., A. F. M. Smith, and W. E. Strawderman. 1994. Bayesian estimation for the Three-Parameter weibull distribution with tree diameter data. Biometrics 50 (1):254–69. doi:10.2307/2533217.
   Web of Science ®Google Scholar
• Gupta, S. S. 1962. On a selection and ranking procedure for gamma populations. Annals of the Institute of Statistical Mathematics 14 (1):199–212. doi:10.1007/BF02868642.
   Google Scholar
• Gupta, S. S., and J. O. Berger. 2012. Statistical decision theory and related topics V. New York, USA: Springer Science & Business Media.
   Google Scholar
• Guttman, I., and G. C. Tiao. 1964. A bayesian approach to some best population problems. The Annals of Mathematical Statistics 35 (2):825–35. doi:10.1214/aoms/1177703582.
   Google Scholar
• Hoel, D. G., and M. Mazumdar. 1968. An extension of Paulson’s selection procedure. The Annals of Mathematical Statistics 39 (6):2067–74.
   Google Scholar
• Hong, L. J. 2006. Fully sequential indifference-zone selection procedures with variance-dependent sampling. Naval Research Logistics 53 :464–76.
   Web of Science ®Google Scholar
• Hong, L. J., and B. L. Nelson. 2005. The trade-off between sampling and switching: new sequential procedures for indifference-zone selection. IIE Transactions 37 (7):623–34. doi:10.1080/07408170590948486.
   Web of Science ®Google Scholar
• Hong, L. J., and B. L. Nelson. 2007. Selecting the best system when systems are revealed sequentially. IIE Transactions 39 (7):723–34. doi:10.1080/07408170600838415.
   Web of Science ®Google Scholar
• Hussein, K., and S. Panchapakesan. 2001. Simultaneous selection of extreme populations from a set of two-parameter exponential populations. Handbook of Statistic 20 :813–30.
   Google Scholar
• Juang, M. G., and G. Anderson. 2004. A Bayesian method on adaptive preventive maintenance problem. European Journal of Operational Research 155 (2):455–73. doi:10.1016/S0377-2217(02)00856-1.
   Web of Science ®Google Scholar
• Kamps, U. 1995. A concept of generalized order statistics. Stuttgart: Teubner.
   Google Scholar
• Kim, S. H., and B. L. Nelson. 2001. A fully sequential procedure for indifference-zone selection in simulation. ACM Transactions on Modeling and Computer Simulation 11 (3):251–73. doi:10.1145/502109.502111.
   Google Scholar
• Lai, Y., Huang, T. H. H. and Lin Y. P. 2012. Selecting the best exponential populations in terms of reliability: Empirical bayes approach. Tamsui Oxford Journal of Information and Mathematical Sciences 28 (3):327–40.
   Google Scholar
• Lam, K., and C. K. Nag. 1990. Two-stage procedures for comparing several exponential populations with a control when the scale parameters are unknown and unequal. Sequential Analysis: Design Methods and Applications 9 (2):151–64. doi:10.1080/07474949008836202.
   Google Scholar
• Lawless, J. F. 2011. Statistical models and methods for lifetime data. New Jersey, USA: John Wiley & Sons.
   Google Scholar
• Lindqvist, B. H. 2006. On the statistical modeling and analysis of repairable systems. Statistical Science 21 (4):532–51. doi:10.1214/088342306000000448.
   Web of Science ®Google Scholar
• Mazzuchi, T. A., and R. Soyer. 1996. A bayesian perspective on some replacement strategies. Reliability Engineering & System Safety 51 (3):295–303. doi:10.1016/0951-8320(95)00077-1.
   Web of Science ®Google Scholar
• Paulson, E. 1964. A sequential procedure for selecting the population with the largest mean from k normal populations. The Annals of Mathematical Statistics 35 (1):174–80. doi:10.1214/aoms/1177703739.
   Google Scholar
• Pichitlamken, J., B. L. Nelson, and L. J. Hong. 2006. A sequential procedure for neighborhood selection-of-the-best in optimization via simulation. European Journal of Operational Research 173 (1):283–98. doi:10.1016/j.ejor.2004.12.010.
   Web of Science ®Google Scholar
• Proschan, F. 1963. Theoretical explanation of observed decreasing failure rate. Technometrics 5 (3):375–83. doi:10.1080/00401706.1963.10490105.
   Web of Science ®Google Scholar
• Rinne, H. 2009. The weibull distribution: A handbook. London: Chapman and Hall.
   Google Scholar
• Wen, M. J., L. C. Huang, and J. Zhong. 2017. Single-stage sampling procedure of the t best populations under heteroscedasticity. Communications in Statistics-Theory and Methods 46 (18):9265–73. doi:10.1080/03610926.2016.1206935.
   Web of Science ®Google Scholar
• Wetherill, G. B., and J. B. Ofosu. 1974. Selection of the best of k normal populations. Journal of Royal Statistical Society. Series C 23 (3):253–77. doi:10.2307/2347119.
   Web of Science ®Google Scholar