References
- Chhikara, R. S., and J. L. Folks. 1989. The inverse Gaussian distribution: Theorem, methodology, and application. New York: Marcel Dekker.
- Elsayed, E. A., and C. K. Chan. 1990. Estimation of thin-oxide reliability using proportional hazards models. IEEE Transactions on Reliability 39 (3):329–35. doi:10.1109/24.103013.
- Fan, T. H., and C. H. Chen. 2017. A Bayesian predictive analysis of step-stress accelerated tests in gamma degradation-based processes. Quality and Reliability Engineering International 33 (7):1417–24. doi:10.1002/qre.2114.
- Hu, C. H., M. Y. Lee, and J. Tang. 2015. Optimum step-stress accelerated degradation test for Wiener degradation process under constraints. European Journal of Operational Research 241 (2):412–21. doi:10.1016/j.ejor.2014.09.003.
- Lee, M. Y., C. H. Hu, and J. Tang. 2017. A two-stage latent variable estimation procedure for time-censored accelerated degradation tests. IEEE Transactions on Reliability 66 (4):1266–79. doi:10.1109/TR.2017.2731680.
- Liao, C. M., and S. T. Tseng. 2006. Optimal design for step-stress accelerated degradation tests. IEEE Transactions on Reliability 55 (1):59–66. doi:10.1109/TR.2005.863811.
- Ling, M. H., K. L. Tsui, and N. Balakrishnan. 2015. Accelerated degradation analysis for the quality of a system based on the gamma process. IEEE Transactions on Reliability 64 (1):463–72. doi:10.1109/TR.2014.2337071.
- Meeker, W. Q., and A. L. Escobar. 1998. Statistical methods for reliability data. New York: Wiley.
- Mudholkar, G. S., and R. Natarajan. 1999. Approximations for the inverse Gaussian probabilities and percentiles. Communications in Statistics - Simulation and Computation 28 (4):1051–71. doi:10.1080/03610919908813592.
- Ng, H. K. T., N. Balakrishnan, and P. S. Chan. 2007. Optimal sample size allocation for tests with multiple levels of stress with extreme value regression. Naval Research Logistics 54 (3):237–49. doi:10.1002/nav.20207.
- Pan, R., and T. Crispin. 2011. A hierarchical modeling approach to accelerated degradation testing data analysis: A case study. Quality and Reliability Engineering International 27 (2):229–37. doi:10.1002/qre.1100.
- Pan, Z., and Q. Sun. 2014. Optimal design for step-stress accelerated degradation test with multiple performance characteristics based on gamma processes. Communications in Statistics - Simulation and Computation 43 (2):298–314. doi:10.1080/03610918.2012.700749.
- Park, C., and W. J. Padgett. 2005. Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis 11 (4):511–27. doi:10.1007/s10985-005-5237-8.
- Si, X. S., W. Wang, C. H. Hu, and D. H. Zhou. 2011. Remaining useful life estimation – A review on the statistical data driven approaches. European Journal of Operational Research 213 (1):1–14. doi:10.1016/j.ejor.2010.11.018.
- Tsai, C. C., C. T. Lin, and N. Balakrishnan. 2015. Optimal design for accelerated-stress acceptance test based on Wiener process. IEEE Transactions on Reliability 64 (2):603–12. doi:10.1109/TR.2015.2410191.
- Tsai, C. C., S. T. Tseng, and N. Balakrishnan. 2011. Mis-specification analyses of gamma and Wiener degradation processes. Journal of Statistical Planning and Inference 141 (12):3725–35. doi:10.1016/j.jspi.2011.06.008.
- Tsai, T.-R., W.-Y. Sung, Y. L. Lio, S. I. Chang, and J.-C. Lu. 2016. Optimal two-variable accelerated degradation test plan for gamma degradation processes. IEEE Transactions on Reliability 65 (1):459–67. doi:10.1109/TR.2015.2435774.
- Tseng, S. T., N. Balakrishnan, and C. C. Tsai. 2009. Optimal step-stress accelerated degradation test plan for Gamma degradation processes. IEEE Transactions on Reliability 58:611–18. doi:10.1109/TR.2009.2033734.
- Tseng, S. T., J. Tang, and I. H. Ku. 2003. Determination of burn-in parameters and residual life for highly reliable products. Naval Research Logistics 50 (1):1–14. doi:10.1002/nav.10042.
- Wang, X. 2010. Wiener process with random effects for degradation data. Journal of Multivariate Analysis 101 (2):340–51. doi:10.1016/j.jmva.2008.12.007.
- Wang, X., N. Balakrishnan, and B. Guo. 2016. Mis-specification analyses of nonlinear Wiener process-based degradation models. Communications in Statistics - Simulation and Computation 45 (3):814–32. doi:10.1080/03610918.2013.875566.
- Wang, X., and D. Xu. 2010. An Inverse Gaussian process model for degradation data. Technometrics 52 (2):188–97. doi:10.1198/TECH.2009.08197.
- Wang, Z., J. Li, X. Ma, Y. Zhang, H. Fu, and S. Krishnaswamy. 2017. A generalized Wiener process degradation model with two transformed time scales. Quality and Reliability Engineering International 33 (4):693–708. doi:10.1002/qre.2049.
- White, H. 1982. Maximum likelihood estimation of misspecified models. Econometrica 50 (1):1–25. doi:10.2307/1912526.
- Xiao, X., and Z. Ye. 2016. Optimal design for destructive degradation tests with random initial degradation values using the Wiener process. IEEE Transactions on Reliability 65 (3):1327–42. doi:10.1109/TR.2016.2575442.
- Ye, Z. S., M. Xie, L. C. Tang, and Y. Shen. 2012. Degradation-based burn-in planning under competing risks. Technometrics 54 (2):159–68. doi:10.1080/00401706.2012.676946.
- Yu, H. F., and S. T. Tseng. 1999. Designing a degradation experiment. Naval Research Logistics 46 (6):689–706. doi:10.1002/(SICI)1520-6750(199909)46:6<689::AID-NAV6>3.0.CO;2-N.
- Zhang, C., X. Lu, Y. Tan, and Y. Wang. 2015. Reliability demonstration methodology for products with Gamma process by optimal accelerated degradation testing. Reliability Engineering & System Safety 142:369–77. doi:10.1016/j.ress.2015.05.011.
- Zhang, K., and J. Xiao. 2018. Time-dependent reliability analysis on carbonation behavior of recycled aggregate concrete based on Gamma process. Construction and Building Materials 158:378–88. doi:10.1016/j.conbuildmat.2017.09.191.
- Zhang, Z., X. Si, C. Hu, and Y. Lei. 2018. Degradation data analysis and remaining useful life estimation: A review on wiener-process-based methods. European Journal of Operational Research 271 (3):775–96. doi:10.1016/j.ejor.2018.02.033.