Modelling degradation with multiple accelerated processes

References

• Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. doi: 10.1109/TAC.1974.1100705.
   Web of Science ®Google Scholar
• Bagdonavicius, V., & Nikulin, M. S. (2000). Estimation in degradation models with explanatory variables. Lifetime Data Analysis, 7, 85–103. doi: 10.1023/A:1009629311100.
   Web of Science ®Google Scholar
• Ebrahem, M. A. -H., Alodat, M. T., & Arman, A. (2009). Estimating the time-to-failure distribution of a linear degradation model using a Bayesian approach. Applied Mathematical Sciences, 3, 27–42.
   Google Scholar
• Fink, D. (1997). A compendium of conjugate priors. Bozeman, MT: Environmental Statistics Group, Department of Biology, Montana State University.
   Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2009). Bayesian data analysis, 2nd edition. Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Genest, C. & Favre, A. C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12, 347–368. doi: 10.1061/(asce)1084-0699(2007)12:4(347).
   Web of Science ®Google Scholar
• Haghighi, F., & Rad, N. (2011). Parametric degradation model with multiple competing risks. Quality Technology and Quantitative Management, 8, 389–400. doi: 10.1080/16843703.2011.11673265.
   Web of Science ®Google Scholar
• Jararha, A. J., Ebrahem, M. A. -H., & Al-Masri, A. Q. (2011). Estimating the parameters of degradation models when error terms are autocorrelated. Austrian Journal of Statistics, 40, 191–200.
   Google Scholar
• Kelly, D. L. (2007). Using copulas to model dependence in simulation risk assessment. ASME International Mechanical Engineering Congress and Exposition, 1-9. Seattle, Washington.
   Google Scholar
• Kruschke, J. K. (2011). Doing Bayesian data analysis: a tutorial with R and BUGS, 1st edition. Oxford: Elsevier.
   Google Scholar
• Lawless, J., & Crowder, M. (2004). Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Analysis, 10, 213–227. doi: 10.1023/b:lida.0000036389.14073.dd.
   PubMed Web of Science ®Google Scholar
• Li, W., & Pham, H. (2005). Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Transactions on Reliability, 54, 297–303. doi: 10.1109/tr.2005.847278.
   Web of Science ®Google Scholar
• Liu, X., Al-Khalifa, K. N., Elsayed, E. A., & Coit, D. W. (2014). Criticality measures for components with multi-dimensional degradation. IEE Transactions, 46, 987–998. doi: 10.1080/0740817x.2013.851433.
   Web of Science ®Google Scholar
• Lu, C. J., & 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
• Lu, C. J., Meeker, W. Q., & Escobar, L. A. (1996). A comparison of degradation and failure-time analysis methods for estimating a time-to-failure distribution. Statistica Sinica, 6, 531–546.
   Web of Science ®Google Scholar
• Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique, and future directions. Statistics in Medicine, 28, 3049–3067. doi: 10.1002/sim.3680.
   PubMed Web of Science ®Google Scholar
• Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data, 1st edition. New York: John Wiley & Sons.
   Google Scholar
• Naya, S., Cao, R., López-de-Ullibarri, I., Artiaga, R., Barbadillo, F., & García, A. (2006). Logistic mixture model vs Arrhenius for kinetic study of degradation of materials by dynamic thermogravimetric analysis. Journal of Chemometrics, 20, 158–163. doi: 10.1002/cem.1023.
   Web of Science ®Google Scholar
• Nelsen, R. B. (2006). An introduction to copulas, 2nd edition. New York: Springer.
   Google Scholar
• Nelson, W. B. (1990). Accelerated testing, statistical models, test plans and data analysis. New York: John Wiley & Sons.
   Google Scholar
• Padgett, W. J., & Tomlinson, M. A. (2004). Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Analysis, 10, 191–206. doi: 10.1023/b:lida.0000030203.49001.b6.
   PubMed Web of Science ®Google Scholar
• Pan, Z., & Balakrishnan, N. (2011). Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes. Reliability Engineering and System Safety, 96, 949–957. doi: 10.1016/j.ress.2011.03.014.
   Web of Science ®Google Scholar
• Park, C., & Padgett, W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis, 11, 511–527. doi: 10.1007/s10985-005-5237-8.
   PubMed Web of Science ®Google Scholar
• Park, C., & Padgett, W. J. (2006). Stochastic degradation models with several accelerating variables. IEEE Transactions on Reliability, 55, 379–390. doi: 10.1109/tr.2006.874937.
   Web of Science ®Google Scholar
• Pinheiro, J., & Bates, D. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12–35. doi: 10.2307/1390625.
   Google Scholar
• Rodgers, J. L., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. The American Statistician, 42, 59–66. doi: 10.2307/2685263.
   Web of Science ®Google Scholar
• Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464. doi: 10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Song, S., Coit, D. W., & Feng, Q. (2014). Reliability for systems of degrading components with distinct component shock sets. Reliability Engineering and System Safety, 132, 115–124. doi: 10.1016/j.ress.2014.06.020.
   Web of Science ®Google Scholar
• Song, S., Coit, D. W., Feng, Q., & Peng, H. (2014). Reliability analysis for multi-component systems subject to multiple dependent competing failure processes. IEEE Transactions on Reliability, 63, 331–345. doi: 10.1109/tr.2014.2299693.
   Web of Science ®Google Scholar
• Wang, Y., & Pham, H. (2012). Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas. IEEE Transactions on Reliability, 61, 13–22. doi: 10.1109/tr.2011.2170253.
   Web of Science ®Google Scholar
• Yu, H. -F. (2003). Designing an accelerated degradation experiment by optimizing the estimation of the percentile. Quality and Reliability Engineering International, 19, 197–214. doi: 10.1002/qre.518.
   Web of Science ®Google Scholar
• Zhao, W., & Elsayed, E. A. (2004). An accelerated life testing model involving performance degradation. Proceedings Annual Reliability and Maintainability Symposium, Los Angeles, CA.
   Google Scholar
• Zhou, J., Pan, Z., & Sun, Q. (2010). Bivariate degradation modeling based on gamma process. Proceedings of the World Congress on Engineering, vol. III. London, U.K.
   Google Scholar