Multivariate time-between-events monitoring: An overview and some overlooked underlying complexities

References

• Ali, S., and A. Pievatolo. 2016. High quality process monitoring using a class of inter-arrival time distributions of the renewal process. Computers & Industrial Engineering 94:45–62. doi:10.1016/j.cie.2016.01.012.
   Web of Science ®Google Scholar
• Ali, S., A. Pievatolo, and R. Göb. 2016. An overview of control charts for high‐quality processes. Quality and Reliability Engineering International 32 (7):2171–89. doi:10.1002/qre.1957.
   Web of Science ®Google Scholar
• Balakrishnan, N., and C. D. Lai. 2009. Continuous bivariate distributions. 2nd ed. New York: Springer.
   Google Scholar
• Bersimis, S., S. Psarakis, and J. Panaretos. 2007. Multivariate statistical process control charts: An overview. Quality and Reliability Engineering International 23 (5):517–43. doi:10.1002/qre.829.
   Web of Science ®Google Scholar
• Bersimis, S., A. Sgora, and S. Psarakis. 2018. The application of multivariate statistical process monitoring in non-industrial processes. Quality Technology & Quantitative Management 15 (4):526–49. doi:10.1080/16843703.2016.1226711.
   Web of Science ®Google Scholar
• Block, H. W., and A. P. Basu. 1974. A continuous, bivariate exponential extension. Journal of the American Statistical Association 69 (348):1031–7. doi:10.1080/01621459.1974.10480249.
   Web of Science ®Google Scholar
• Byar, D. P. 1980. The Veterans administration study of chemoprophylaxis for recurrent stage I bladder tumors: Comparisons of placebo, pyridoxine, and topical thiotepa. In Bladder tumors and other topics in urological oncology, ed. Pavone-Macaluso M., Smith P.H., Edsmyr F. Ettore Majorana International Science Series (Life Sciences), vol 1. Boston, MA: Springer.
   Google Scholar
• Chen, J.-T. 2014. A Shewhart-type control scheme to monitor Weibull data without subgrouping. Quality and Reliability Engineering International 30 (8):1197–214. doi:10.1002/qre.1542.
   Web of Science ®Google Scholar
• Chiou, S., G. Xu, J. Yan, and C.-Y. Huang. 2018. Semiparametric estimation of the accelerated mean model with panel count data under informative examination times. Biometrics 74 (3):944–53. doi:10.1111/biom.12840.
   PubMed Web of Science ®Google Scholar
• Cox, D. R., and V. Isham. 1977. A bivariate point process connected with electronic counters. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 356 (1685):149–60. doi:10.1098/rspa.1977.0126.
   Web of Science ®Google Scholar
• Cozzucoli, P. C., and M. Marozzi. 2018. Monitoring multivariate Poisson processes: A review and some new results. Quality Technology & Quantitative Management 15 (1):53–68. doi:10.1080/16843703.2017.1304035.
   Web of Science ®Google Scholar
• Daley, D., and D. Jones. 2007. An introduction to the theory of point processes: Volume II: General theory and structure. Newyork: Springer Science & Business Media.
   Google Scholar
• Dhini, A., and I. Surjandari. 2016, January. Review on some multivariate statistical process control methods for process monitoring. In Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management, 754–759.
   Google Scholar
• Doss, H. 1989. On estimating the dependence between two point processes. The Annals of Statistics 17 (2):749–63. doi:10.1214/aos/1176347140.
   Web of Science ®Google Scholar
• Downton, F. 1970. Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society: Series B (Methodological) 32 (3):408–17. doi:10.1111/j.2517-6161.1970.tb00852.x.
   Web of Science ®Google Scholar
• Flury, M. I., and M. B. Quaglino. 2018. Multivariate EWMA control chart with highly asymmetric gamma distributions. Quality Technology & Quantitative Management 15 (2):230–52. doi:10.1080/16843703.2016.1208937.
   Web of Science ®Google Scholar
• Freund, J. E. 1961. A bivariate extension of the exponential distribution. Journal of the American Statistical Association 56 (296):971–7. doi:10.1080/01621459.1961.10482138.
   Web of Science ®Google Scholar
• Friday, D. S., and G. P. Patil. 1977. A bivariate exponential model with applications to reliability and computer generation of random variables. In The theory and applications of reliability with emphasis on bayesian and nonparametric methods, ed. C. Tsokos and I. N. Shimi, 527–49. New York: Academic Press.
   Google Scholar
• Frisén, M., E. Andersson, and L. Schiöler. 2010. Evaluation of multivariate surveillance. Journal of Applied Statistics 37 (12):2089–100. doi:10.1080/02664760903222208.
   Web of Science ®Google Scholar
• Gan, F. F. 1998. Designs of one-and two-sided exponential EWMA charts. Journal of Quality Technology 30 (1):55–69. doi:10.1080/00224065.1998.11979819.
   Web of Science ®Google Scholar
• Gross, A. J., and C. F. Lam. 1981. Paired observations from a survival distribution. Biometrics 37 (3):505–11. doi:10.2307/2530563.
   Web of Science ®Google Scholar
• Gumbel, E. J. 1960. Bivariate exponential distributions. Journal of the American Statistical Association 55 (292):698–707. doi:10.1080/01621459.1960.10483368.
   Web of Science ®Google Scholar
• Hawkes, A. G. 1971. Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1):83–90. doi:10.1093/biomet/58.1.83.
   Web of Science ®Google Scholar
• Hougaard, P. 1986. A class of multivariate failure time distributions. Biometrika 73 (3):671–8. doi:10.1093/biomet/73.3.671.
   Web of Science ®Google Scholar
• Huster, W. J., R. Brookmeyer, and S. G. Self. 1989. Modelling paired survival data with covariates. Biometrics 45 (1):145–56. doi:10.2307/2532041.
   PubMed Web of Science ®Google Scholar
• Jarrett, R. G. 1979. A note on the intervals between coal-mining disasters. Biometrika 66 (1):191–3. doi:10.1093/biomet/66.1.191.
   Web of Science ®Google Scholar
• Joe, H. 2014. Dependence modeling with copulas. Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Jones-Farmer, L. A., W. H. Woodall, S. H. Steiner, and C. W. Champ. 2014. An overview of phase I analysis for process improvement and monitoring. Journal of Quality Technology 46 (3):265–80. doi:10.1080/00224065.2014.11917969.
   Web of Science ®Google Scholar
• Khan, N., M. Aslam, M. S. Aldosari, and C. H. Jun. 2018. A multivariate control chart for monitoring several exponential quality characteristics using EWMA. IEEE Access. 6:70349–58. doi:10.1109/ACCESS.2018.2881054.
   Web of Science ®Google Scholar
• Kotz, S., N. Balakrishnan, and N. L. Johnson. 2000. Continuous Multivariate distributions. 2nd ed. New York: John Wiley and Sons.
   Google Scholar
• Kuvattana, S., and S. Sukparungsee. 2015, October. Comparative the performance of control charts based on copulas. In The World Congress on Engineering and Computer Science, 47–58. Singapore: Springer.
   Google Scholar
• Li, Y., J. Sun, and S. Song. 2012. Statistical analysis of bivariate failure time data with Marshall-Olkin Weibull models. Computational Statistics & Data Analysis 56 (6):2041–50. doi:10.1016/j.csda.2011.12.010.
   PubMed Web of Science ®Google Scholar
• Li, S., Y. Xie, M. Farajtabar, A. Verma, and L. Song. 2017. Detecting changes in dynamic events over networks. IEEE Transactions on Signal and Information Processing over Networks 3 (2):346–59. doi:10.1109/TSIPN.2017.2696264.
   Web of Science ®Google Scholar
• Li, Z., C. Zou, Z. Gong, and Z. Wang. 2014. The computation of average run length and average time to signal: An overview. Journal of Statistical Computation and Simulation 84 (8):1779–802. doi:10.1080/00949655.2013.766737.
   Web of Science ®Google Scholar
• Lowry, C. A., W. H. Woodall, C. W. Champ, and S. E. Rigdon. 1992. A multivariate exponentially weighted moving average control chart. Technometrics 34 (1):46–53. doi:10.1080/00401706.1992.10485232.
   Web of Science ®Google Scholar
• Lu, J., and G. K. Bhattacharyya. 1991. Inference Procedure for Bivariate exponential distributions. Statistics & Probability Letters 12 (1):37–50. doi:10.1016/0167-7152(91)90162-K.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62 (317):30–44. doi:10.1080/01621459.1967.10482885.
   Web of Science ®Google Scholar
• Mukherjee, A., Y. Cheng, and M. Gong. 2018. A new nonparametric scheme for simultaneous monitoring of bivariate processes and its application in monitoring service quality. Quality Technology & Quantitative Management 15 (1):143–56. doi:10.1080/16843703.2017.1312808.
   Web of Science ®Google Scholar
• Nelsen, R. B. 2006. An introduction to copulas. 2nd ed. New York: Springer.
   Google Scholar
• Nelson, W. B. 1982. Applied life data analysis, 187–8. New York: John Wiley & Sons, Inc.
   Google Scholar
• Pascual, F. G., and S. B. Akhundjanov. 2020. Copula-based control charts for monitoring multivariate Poisson processes with application to Hepatitis C counts. Journal of Quality Technology 52 (2):128–44. doi:10.1080/00224065.2019.1571337.
   Web of Science ®Google Scholar
• Proschan, F., and Sullo. P. 1976. Estimating the parameters of a multivariate exponential distribution. Journal of the American Statistical Association 71 (354):465–72. doi:10.1080/01621459.1976.10480370.
   Web of Science ®Google Scholar
• Raftery, A. E. 1984. A continuous multivariate exponential distribution. Communications in Statistics - Theory and Methods 13 (8):947–65. doi:10.1080/03610928408828733.
   Web of Science ®Google Scholar
• Santiago, E., and J. Smith. 2013. Control charts based on the exponential distribution: Adapting runs rules for the t chart. Quality Engineering 25 (2):85–96. doi:10.1080/08982112.2012.740646.
   Web of Science ®Google Scholar
• Sarkar, S. K. 1987. A continuous bivariate exponential distribution. Journal of the American Statistical Association 82 (398):667–75. doi:10.1080/01621459.1987.10478481.
   Web of Science ®Google Scholar
• Schuh, A., J. A. Camelio, and W. H. Woodall. 2014. Control charts for accident frequency: A motivation for real-time occupational safety monitoring. International Journal of Injury Control and Safety Promotion 21 (2):154–63. doi:10.1080/17457300.2013.792285.
   PubMed Web of Science ®Google Scholar
• Schuh, A., W. H. Woodall, and J. A. Camelio. 2013. The effect of aggregating data when monitoring a Poisson process. Journal of Quality Technology 45 (3):260–72. doi:10.1080/00224065.2013.11917937.
   Web of Science ®Google Scholar
• Sparks, R., B. Jin, S. Karimi, C. Paris, and C. R. MacIntyre. 2019. Real-time monitoring of events applied to syndromic surveillance. Quality Engineering 31 (1):73–90. doi:10.1080/08982112.2018.1537443.
   Web of Science ®Google Scholar
• Sparks, R. S. 2019. An approach to monitoring multivariate time between events. Presentation at the ISI World Statistics Conference, 19 August.
   Google Scholar
• Sukparungsee, S.,. S. Kuvattana, P. Busababodhin, and Y. Areepong. 2017. Multivariate copulas on the MCUSUM control chart. Cogent Mathematics 4 (1):1342318. doi:10.1080/23311835.2017.1342318.
   Web of Science ®Google Scholar
• Sukparungsee, S.,. S. Kuvattana, P. Busababodhin, and Y. Areepong. 2018. Bivariate copulas on the Hotelling's T2 control chart. Communications in Statistics - Simulation and Computation 47 (2):413–9. doi:10.1080/03610918.2016.1228958.
   Web of Science ®Google Scholar
• Tosch, T. J., and P. T. Holmes. 1980. A bivariate failure model. Journal of the American Statistical Association 75 (370):415–7. doi:10.1080/01621459.1980.10477487.
   Web of Science ®Google Scholar
• Woodall, W. H., and D. C. Montgomery. 2014. Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology 46 (1):78–94. doi:10.1080/00224065.2014.11917955.
   Web of Science ®Google Scholar
• Xie, Y., M. Xie, and T. N. Goh. 2011. Two MEWMA charts for Gumbel's bivariate exponential distribution. Journal of Quality Technology 43 (1):50–65. doi:10.1080/00224065.2011.11917845.
   Web of Science ®Google Scholar
• Zwetsloot, I. M., and W. H. Woodall. 2020. A review of some sampling and aggregation strategies for basic statistical process monitoring [with discussion]. Journal of Quality Technology. doi:10.1080/00224065.2019.1611354.
   Web of Science ®Google Scholar