Student-t Processes for Degradation Analysis

References

• Almeida, C. P. (2011), “Methods of Numerical Estimation for Degradation Models With Nonnormal Random Effects,” unpublished master dissertation, Federal University of Minas Gerais, Department of Statistics.
   Google Scholar
• Bagdonavičius, V., and Nikulin, M. S. (2001a), Accelerated Life Models: Modeling and Statistical Analysis, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Bagdonavičius, V., and Nikulin, M. S. (2001b), “Estimation in Degradation Models With Explanatory Variables,” Lifetime Data Analysis, 7, 85–103.
   PubMed Web of Science ®Google Scholar
• Box, G. E. P., and Tiao, G. C. (2011), Bayesian Inference in Statistical Analysis, New York: Wiley.
   Google Scholar
• Cheng, Y. S., and Peng, C. Y. (2012), “Integrated Degradation Models in R Using iDEMO,” Journal of Statistical Software, 49, 1–22. DOI: 10.18637/jss.v049.i02.
   Web of Science ®Google Scholar
• Diggle, P. J., Heagerty, P., Liang, K. Y., and Zeger, S. L. (2002), Analysis of Longitudinal Data (2nd ed.), London: Oxford University Press.
   Google Scholar
• Di Nardo, E., Nobile, A. G., Pirozzi, E., and Ricciardi, L. M. (2001), “A Computational Approach to First-Passage-Time Problems for Gauss-Markov Processes,” Advances in Applied Probability, 33, 453–482. DOI: 10.1017/S0001867800010892.
   Web of Science ®Google Scholar
• Doksum, K. A., and Hóyland, A. (1992), “Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution,” Technometrics, 34, 74–82. DOI: 10.2307/1269554.
   Web of Science ®Google Scholar
• Doksum, K. A., and Normand, S. L. T. (1995), “Gaussian Models for Degradation Processes—Part I: Methods for the Analysis of Biomarker Data,” Lifetime Data Analysis, 1, 131–144.
   PubMedGoogle Scholar
• Hamada, M. S., Wilson, A. G., Reese, C. S., and Martz, H. F. (2008), Bayesian Reliability, New York: Springer-Verlag.
   Google Scholar
• Hong, Y., Duan, Y., Meeker, W. Q., Stanley, D. L., and Gu, X. (2015), “Statistical Methods for Degradation Data With Dynamic Covariates Information and an Application to Outdoor Weathering Data,” Technometrics, 57, 180–193. DOI: 10.1080/00401706.2014.915891.
   Web of Science ®Google Scholar
• Lange, K. L., Little, R. J. A., and Taylor, J. M. G. (1989), “Robust Statistical Modeling Using the t Distribution,” Journal of the American Statistical Association, 84, 881–896. DOI: 10.2307/2290063.
   Web of Science ®Google Scholar
• Lawless, J., and Crowder, M. (2004), “Covariates and Random Effects in a Gamma Process Model With Application to Degradation and Failure,” Lifetime Data Analysis, 10, 213–227.
   PubMed Web of Science ®Google Scholar
• Lu, C. J., and Meeker, W. Q. (1993), “Using Degradation Measures to Estimate a Time-to-Failure Distribution,” Technometrics, 35, 161–174. DOI: 10.1080/00401706.1993.10485038.
   Web of Science ®Google Scholar
• Meeker, W. Q., and Escobar, L. A. (1998), Statistical Methods for Reliability Data, New York: Wiley.
   Google Scholar
• Nelson, W. (1990), Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, New York: Wiley.
   Google Scholar
• Ott, H. W. (1988), Noise Reduction Techniques in Electronic Systems (2nd ed.), New York: Wiley.
   Google Scholar
• Peng, C. Y. (2015), “Inverse Gaussian Processes With Random Effects and Explanatory Variables for Degradation Data,” Technometrics, 57, 100–111. DOI: 10.1080/00401706.2013.879077.
   Web of Science ®Google Scholar
• Peng, C. Y., and Cheng, Y. S. (2016), “Threshold Degradation in R Using iDEMO,” in Computational Network Analysis With R: Applications in Biology, Medicine and Chemistry, eds. M. Dehmer, Y. Shi, and F. Emmert-Streib, Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, pp. 83–124.
   Google Scholar
• Peng, C. Y., and Tseng, S. T. (2009), “Misspecification Analysis of Linear Degradation Models,” IEEE Transactions on Reliability, 58, 444–455.
   Web of Science ®Google Scholar
• Pinheiro, J. C., Liu, C., and Wu, Y. N. (2001), “Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution,” Journal of Computational and Graphical Statistics, 10, 249–276. DOI: 10.1198/10618600152628059.
   Web of Science ®Google Scholar
• R Core Team (2019), R: A Language and Environment for Statistical Computing, Vienna: R Foundation for Statistical Computing, available at http://www.R-project.org/.
   Google Scholar
• Ricciardi, L. M., and Sato, S. (1983), “A Note on First Passage Time for Gaussian Processes and Varying Boundaries,” IEEE Transactions on Information Theory, 29, 454–457. DOI: 10.1109/TIT.1983.1056654.
   Web of Science ®Google Scholar
• Singpurwalla, N. D. (1995), “Survival in Dynamic Environments,” Statistical Science, 10, 86–103. DOI: 10.1214/ss/1177010132.
   Web of Science ®Google Scholar
• Sobczyk, K., and Spencer, B. F., Jr. (1992), Random Fatigue: From Data to Theory, San Diego, CA: Academic Press.
   Google Scholar
• Tsai, C. C., Tseng, S. T., and Balakrishnan, N. (2012), “Optimal Design for Gamma Degradation Processes With Random Effects,” IEEE Transactions on Reliability, 61, 604–613. DOI: 10.1109/TR.2012.2194351.
   Web of Science ®Google Scholar
• Tseng, S. T., and Lee, I. C. (2016), “Optimum Allocation Rule for Accelerated Degradation Tests With a Class of Exponential-Dispersion Degradation Models,” Technometrics, 58, 244–254. DOI: 10.1080/00401706.2015.1033109.
   Web of Science ®Google Scholar
• Wang, X. (2010), “Wiener Processes With Random Effects for Degradation Data,” Journal of Multivariate Analysis, 101, 340–351. DOI: 10.1016/j.jmva.2008.12.007.
   Web of Science ®Google Scholar
• Wang, X., and Xu, D. (2010), “An Inverse Gaussian Process Model for Degradation Data,” Technometrics, 52, 188–197. DOI: 10.1198/TECH.2009.08197.
   Web of Science ®Google Scholar
• Weaver, B. P., Meeker, W. Q., Escobar, L. A., and Wendelberger, J. (2013), “Methods for Planning Repeated Measures Degradation Studies,” Technometrics, 55, 122–134. DOI: 10.1080/00401706.2012.715838.
   Web of Science ®Google Scholar
• Whitmore, G. A. (1995), “Estimating Degradation by a Wiener Diffusion Process Subject to Measurement Error,” Lifetime Data Analysis, 1, 307–319. DOI: 10.1007/BF00985762.
   PubMedGoogle Scholar
• Whitmore, G. A., and Schenkelberg, F. (1997), “Modeling Accelerated Degradation Data Using Wiener Diffusion With a Time Scale Transformation,” Lifetime Data Analysis, 3, 27–45.
   PubMedGoogle Scholar
• Wu, S. J., and Shao, J. (1999), “Reliability Analysis Using the Least Squares Method in Nonlinear Mixed-Effect Degradation Models,” Statistica Sinica, 9, 855–877.
   Web of Science ®Google Scholar
• Xie, Y., King, C., Hong, Y., and Yang, Q. (2018), “Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis,” Technometrics, 60, 222–234. DOI: 10.1080/00401706.2017.1321584.
   Web of Science ®Google Scholar
• Ye, Z., and Chen, N. (2014), “The Inverse Gaussian Process as a Degradation Model,” Technometrics, 56, 302–311. DOI: 10.1080/00401706.2013.830074.
   Web of Science ®Google Scholar
• Zhou, R., Serban, N., Gebraeel, N., and Müller, H. G. (2014), “A Functional Time Warping Approach to Modeling and Monitoring Truncated Degradation Signals,” Technometrics, 56, 67–77. DOI: 10.1080/00401706.2013.805661.
   Web of Science ®Google Scholar
• Zhuang, D. (1994), “Degradation Failure Model and Its Statistical Analysis,” unpublished Ph.D. dissertation, East China Normal University, Department of Mathematical Statistics.
   Google Scholar