CUSUM control schemes for monitoring Wiener processes

References

• Alberto Rodriguez-Picon, L., A. Patricia Rodriguez-Picon, L. Carlos Mendez-Gonzalez, M. I. Rodriguez-Borbon, and A. Alvarado-Iniesta. 2018. Degradation modeling based on gamma process models with random effects. Communications in Statistics 47 (6-7):1796–810.
   Google Scholar
• Bae, S. J., T. Yuan, S. Ning, and W. Kuo. 2015. A bayesian approach to modeling two-phase degradation using change-point regression. Reliability Engineering & System Safety 134:66–74. doi:10.1016/j.ress.2014.10.009.
   Web of Science ®Google Scholar
• Brook, D., and D. A. Evans. 1972. An approach to the probability distribution of CUSUM run length. Biometrika 59 (3):539–49. doi:10.1093/biomet/59.3.539.
   Web of Science ®Google Scholar
• Celano, G., P. Castagliola, and E. Trovato. 2012. The economic performance of a CUSUM t control chart for monitoring short production runs. Quality Technology & Quantitative Management 9 (4):329–54. doi:10.1080/16843703.2012.11673297.
   Web of Science ®Google Scholar
• Chen, N., and S. Zhou. 2015. CUSUM statistical monitoring of M/M/1 queues and extensions. Technometrics 57 (2):245–56. doi:10.1080/00401706.2014.923787.
   Web of Science ®Google Scholar
• Garza-Venegas, J. A., V. G. Tercero-Gómez, H. L. Lee, P. Castagliola, and G. Celano. 2018. Effect of autocorrelation estimators on the performance of the X-bar control chart. Journal of Statistical Computation and Simulation 88 (13):2612–30. doi:10.1080/00949655.2018.1479752.
   Web of Science ®Google Scholar
• Hossain, M. P., R. A. Sanusi, M. H. Omar, and M. Riaz. 2019. On designing maxwell CUSUM control chart: An efficient way to monitor failure rates in boring processes. The International Journal of Advanced Manufacturing Technology 100 (5-8):1923–30. doi:10.1007/s00170-018-2679-1.
   Web of Science ®Google Scholar
• Huang, W., L. Shu, W. Jiang, and K. L. Tsui. 2013. Evaluation of run-length distribution for cusum charts under gamma distributions. IIE Transactions 45 (9):981–94. doi:10.1080/0740817X.2012.705455.
   Web of Science ®Google Scholar
• Hussain, S., X. Wang, S. Ahmad, and M. Riaz. 2020. On a class of mixed EWMA-CUSUM median control charts for process monitoring. Quality and Reliability Engineering International 36 (3):910–46. doi:10.1002/qre.2608.
   Web of Science ®Google Scholar
• Ke, X., and Z. Xu. 2016. A model for degradation prediction with change point based on Wiener process. 2015 IEEE International Conference on Industrial Engineering and Engineering Management, Singapore, December 2015. IEEE.
   Google Scholar
• Lucas, J. M., and R. B. Crosier. 1982. Fast initial response for CUSUM quality-control schemes: Give your CUSUM a head start. Technometrics 24 (3):199–205. doi:10.1080/00401706.1982.10487759.
   Web of Science ®Google Scholar
• Nguyen, Q. T., K. P. Tran, P. Castagliola, G. Celano, and S. Lardjane. 2019. One-sided synthetic control charts for monitoring the multivariate coefficient of variation. Journal of Statistical Computation and Simulation 89 (10):1841–62. doi:10.1080/00949655.2019.1600694.
   Web of Science ®Google Scholar
• Page, E. S. 1954. Continuous inspection schemes. Biometrika 41 (1-2):100–15. doi:10.1093/biomet/41.1-2.100.
   Web of Science ®Google Scholar
• Pan, Z., N. Balakrishnan, Q. Sun, and J. Zhou. 2013. Bivariate degradation analysis of products based on wiener processes and copulas. Journal of Statistical Computation and Simulation 83 (7):1316–29. doi:10.1080/00949655.2012.658805.
   Web of Science ®Google Scholar
• Peng, C. Y., and S. T. Tseng. 2009. Mis-specification analysis of linear degradation models. Reliability, IEEE Transactions on Reliability 58 (3):444–55.
   Web of Science ®Google Scholar
• Peng, C. Y., and S. T. Tseng. 2013. Statistical lifetime inference with skew-wiener linear degradation models. IEEE Transactions on Reliability 62 (2):338–50.
   Web of Science ®Google Scholar
• Rafiee, K., Q. Feng, and D. W. Coit. 2017. Reliability analysis and condition-based maintenance for failure processes with degradation-dependent hard failure threshold. Quality and Reliability Engineering International 33 (7):1351–66. doi:10.1002/qre.2109.
   Web of Science ®Google Scholar
• Raji, I. A., N. Abbas, and M. Riaz. 2019. Robust dual-CUSUM control charts for contaminated processes. Communications in Statistics - Simulation and Computation 48 (7):2177–90. doi:10.1080/03610918.2018.1435804.
   Web of Science ®Google Scholar
• Rodríguez-Picón, L., A. Rodríguez-Picón, L. Mendez, M. Rodríguez-Borbón, and A. Alvarado-Iniesta. 2017. Degradation modeling based on gamma process models with random effects. Communications in Statistics - Simulation and Computation 47 (6):1796–810. doi:10.1080/03610918.2017.1324981.
   Web of Science ®Google Scholar
• Sanusi, R. A., N. Abbas, and M. Riaz. 2018. On efficient CUSUM-type control chart for monitoring the process mean using auxiliary information. Quality Technology & Quantitative Management 15 (1):87–105. doi:10.1080/16843703.2017.1304039.
   Web of Science ®Google Scholar
• Si, X. S., W. Wang, C. H. Hu, D. H. Zhou, and M. G. Pecht. 2012. Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE Transactions on Reliability 61 (1):50–67. doi:10.1109/TR.2011.2182221.
   Web of Science ®Google Scholar
• Son, J., Y. Zhang, C. Sankavaram, and S. Zhou. 2015. RUL prediction for individual units based on condition monitoring signals with a change point. IEEE Transactions on Reliability 64 (1):182–96. doi:10.1109/TR.2014.2355531.
   Web of Science ®Google Scholar
• Tang, J., and T. S. Su. 2008. Estimating failure time distribution and its parameters based on intermediate data from a wiener degradation model. Naval Research Logistics 55 (3):265–76. doi:10.1002/nav.20280.
   Web of Science ®Google Scholar
• Wang, X. 2010. Wiener processes with random effects for degradation data. Journal of Multivariate Analysis 101 (2):340–51. doi:10.1016/j.jmva.2008.12.007.
   Web of Science ®Google Scholar
• Wang, X., N. Balakrishnan, and B. Guo. 2014. Residual life estimation based on a generalized wiener process with skew-normal random effects. Communications in Statistics - Simulation and Computation 45 (6):2158–81. doi:10.1080/03610918.2014.894057.
   Web of Science ®Google Scholar
• Wang, X., P. Jiang, B. Guo, and Z. Cheng. 2014. Real-time reliability evaluation for an individual product based on change-point gamma and wiener process. Quality and Reliability Engineering International 30 (4):513–25. doi:10.1002/qre.1504.
   Web of Science ®Google Scholar
• Wen, Y., J. Wu, D. Das, and T. L. Tseng. 2018. Degradation modeling and rul prediction using wiener process subject to multiple change points and unit heterogeneity. Reliability Engineering & System Safety 176:113–24. doi:10.1016/j.ress.2018.04.005.
   Web of Science ®Google Scholar
• Whitmore, G. A., and F. Schenkelberg. 1997. Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Analysis 3 (1):27–45.
   PubMedGoogle Scholar
• Wu, Z., and T. A. Spedding. 2000. A synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology 32 (1):32–38. doi:10.1080/00224065.2000.11979969.
   Web of Science ®Google Scholar
• Xu, S., and D. R. Jeske. 2018. Weighted EWMA charts for monitoring type I censored Weibull lifetimes. Journal of Quality Technology 50 (2):220–30. doi:10.1080/00224065.2018.1436830.
   Web of Science ®Google Scholar
• Ye, Z. S., N. Chen, and Y. Shen. 2015. A new class of wiener process models for degradation analysis. Reliability Engineering & System Safety 139:58–67. doi:10.1016/j.ress.2015.02.005.
   Web of Science ®Google Scholar
• Zhai, Q., P. Chen, L. Hong, and L. Shen. 2018. A random-effects wiener degradation model based on accelerated failure time. Reliability Engineering & System Safety 180:94–103. doi:10.1016/j.ress.2018.07.003.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar