A Multi-Level Trend-Renewal Process for Modeling Systems With Recurrence Data

References

• Berg, A., Meyer, R., and Yu, J. (2004), “Deviance Information Criterion for Comparing Stochastic Volatility Models,” Journal of Business and Economic Statistics, 22, 107–120.
   Web of Science ®Google Scholar
• Brown, M., and Proschan, F. (1983), “Imperfect Repair,” Journal of Applied Probability, 20, 851–859.
   Web of Science ®Google Scholar
• Doyen, L., and Gaudoin, O. (2004), “Classes of Imperfect Repair Models Based on Reduction of Failure Intensity or Virtual Age,” Reliability Engineering and System Safety, 84, 45–56.
   Web of Science ®Google Scholar
• Franz, J., Jokiel-Rokita, A., and Magiera, R. (2014), “Prediction in Trend-renewal Processes for Repairable Systems,” Statistics and Computing, 24, 633–649.
   Web of Science ®Google Scholar
• Gelman, A., Gilks, W. R., and Roberts, G. O. (1997), “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms,” Annals of Applied Probability, 7, 110–120.
   Web of Science ®Google Scholar
• Heggland, K., and Lindqvist, B. (2007), “A Non-parametric Monotone Maximum Likelihood Estimator of Time Trend for Repairable System Data,” Reliability Engineering & System Safety, 92, 575–584.
   Web of Science ®Google Scholar
• Hobert, J. P., and Casella, G. (1996), “The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models,” Journal of the American Statistical Association, 91, 1461–1473.
   Web of Science ®Google Scholar
• Hong, Y., Li, M., and Osborn, B. (2015), “System Unavailability Analysis Based on Window-Observed Recurrent Event Data,” Applied Stochastic Models in Business and Industry, 31, 122–136.
   Web of Science ®Google Scholar
• Hong, Y., and Meeker, W. Q. (2013), “Field-Failure Predictions Based on Failure-Time Data With Dynamic Covariate Information,” Technometrics, 55, 135–149.
   Web of Science ®Google Scholar
• Johnson, V. E., Moosman, A., and Cotter, P. (2005), “A Hierarchical Model for Estimating the Early Reliability of Complex Systems,” IEEE Transactions on Reliability, 54, 224–231.
   Web of Science ®Google Scholar
• Jokiel-Rokita, A., and Magiera, R. (2012), “Estimation of Parameters for Trend-Renewal Processes,” Statistics and Computing, 22, 625–637.
   Web of Science ®Google Scholar
• Kijima, M. (1989), “Some Results for Repairable Systems With General Repair,” Journal of Applied Probability, 26, 89–102.
   Web of Science ®Google Scholar
• Lawless, J., and Thiagarajah, K. (1996), “A Point-Process Model Incorporating Renewals and Time Trends, With Application to Repairable Systems,” Technometrics, 38, 131–138.
   Web of Science ®Google Scholar
• Leemis, L. M. (2004), “Technical Note: Nonparametric Estimation and Variate Generation for a Nonhomogeneous Poisson Process From Event Count Data,” IIE Transactions, 36, 1155–1160.
   Web of Science ®Google Scholar
• Lindqvist, B. (2006), “On the Statistical Modeling and Analysis of Repairable Systems,” Statistical Science, 21, 532–551.
   Web of Science ®Google Scholar
• Lindqvist, B., Elvebakk, G., and Heggland, K. (2003), “The Trend-Renewal Process for Statistical Analysis of Repairable Systems,” Technometrics, 45, 31–44.
   Web of Science ®Google Scholar
• Liu, J., Li, J., and Kim, B. U. (2011), “Bayesian Reliability Modeling of Multi-Level System With Interdependent Subsystems and Components,” IEEE International Conference on Intelligence and Security Informatics, 252–257.
   Google Scholar
• Pietzner, D., and Wienke, A. (2013), “The Trend-Renewal Process: A Useful Model for Medical Recurrence Data,” Statistics in Medicine, 32, 142–152.
   PubMed Web of Science ®Google Scholar
• Roberts, G. O., and Rosenthal, J. S. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367.
   Web of Science ®Google Scholar
• ——— (2009), “Examples of Adaptive MCMC,” Journal of Computational and Graphical Statistics, 18, 349–367.
   Web of Science ®Google Scholar
• Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit,” Journal of the Royal Statistical Society, 64, 583–639.
   Google Scholar
• Wang, H., and Pham, H. (1996), “A Quasi Renewal Process and its Applications in Imperfect Maintenance,” International Journal of Systems Science, 27, 1055–1062.
   Web of Science ®Google Scholar
• Wilson, A. G., Graves, T. L., Hamada, M. S., and Reese, C. S. (2006), “Advances in Data Combination, Analysis and Collection for System Reliability Assessment,” Statistical Science, 21, 514–531.
   Web of Science ®Google Scholar
• Yańez, M., Joglar, F., and Modarres, M. (2002), “Generalized Renewal Process for Analysis of Repairable Systems With Limited Failure Experience,” Reliability Engineering and System Safety, 77, 167–180.
   Web of Science ®Google Scholar
• Yang, Q., Hong, Y., Chen, Y., and Shi, J. (2012), “Failure Profile Analysis of Complex Repairable Systems With Multiple Failure Modes,” IEEE Transactions on Reliability, 61, 180–191.
   Web of Science ®Google Scholar
• Yeh, L. (1988), “Geometric Process and Replacement Problem,” Acta Mathematicae Applicatae Sinica, 4, 366–377.
   Google Scholar
• Yu, Q., Guo, H., and Liao, H. (2013), “An Analytical Approach to Failure Prediction for Systems Subject to General Repairs,” IEEE Transactions on Reliability, 62, 714–721.
   Web of Science ®Google Scholar
• Zhao, R., and Liu, B. (2003), “Renewal Process With Fuzzy Interarrival Times and Rewards,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11, 573–586.
   Web of Science ®Google Scholar