Journal of Quality Engineering and Production Optimization

Journal of Quality Engineering and Production Optimization

Simultaneous monitoring of time between events and their multivariate magnitude

Document Type : Research Paper

Authors
1 Department of Industrial Engineering, Faculty of Engineering, Shahed university, Tehran, Iran
2 Department of Industrial Engineering , Faculty of Engineering, Shahed University, Tehran, Iran
Abstract
Monitoring the time between events without accounting for their magnitudes is an impractical approach. This paper discusses the monitoring of the time between events (TBEs) and their multivariate magnitude (M). The paper explores control charts for the magnitude of events in a multivariate setting, focusing on situations where the magnitude of events has two dimensions. Two statistics are presented for the simultaneous monitoring of the time between events and the multivariate magnitude. The first statistic is a standardized EWMAZ, based on the Shewhart-EWMA approach. The second statistic is a set of three standardized single EWMAs, each used for monitoring TBEs and the two dimensions of magnitude (TSEWMA). The performance of these statistics is evaluated by considering different shifts in the mean of TBE and magnitude under three distinct shift parameter values. The results confirm their effectiveness across various conditions.
Keywords

Abubakar, S. S., Khoo, M. B., Saha, S., & Lee, M. H. (2021). A new exponentially weighted moving average chart with an adaptive control scheme for high yield processes—An application in injection molding process. Quality and Reliability Engineering International, 37(2), 527-540.
Albers, W., & Kallenberg, W. C. (2006). Alternative Shewhart-type charts for grouped observations. Metron, 64(3), 357-375.
Ali, S. (2021). First passage time control charts assuming power law intensity for time to jointly monitor time and magnitude. Quality and Reliability Engineering International, 37(5), 2034-2064.
Ali, S., Zafar, T., Shah, I., & Wang, L. (2020). Cumulative Conforming Control Chart Assuming Discrete Weibull Distribution. IEEE Access, 8, 10123-10133.
Amiri, A., Sogandi, F., & Ayoubi, M. (2018). Simultaneous monitoring of correlated multivariate linear and GLM regression profiles in Phase II. Quality Technology & Quantitative Management, 15(4), 435-458.
Amjadi, N., & Sabri‐Laghaie, K. (2022). Median‐rate control chart for simultaneous monitoring of frequency and magnitude of events. Quality and Reliability Engineering International, 38(1), 89-109.
Aslam, M., Khan, N., Azam, M., & Jun, C. H. (2014). Designing of a new monitoring t-chart using repetitive sampling. Information sciences, 269, 210-216.
Calvin, T. (1983). Quality control techniques for "zero defects". IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 6(3), 323-328.
Chen, Y. K., & Chen, C. Y. (2012). Cumulative Conformance Count Charts with VariableSample Sizes. International Journal of Trade, Economics and Finance, 3(3), 187-193.
Chen, Y. K., & Chiu, F. R. (2023). AX/T Control Chart-Based CBM Model for Service Facility Maintenance. Arabian Journal for Science and Engineering, 48(5), 7207-722.
Di Bucchianico, A., Mooiweer, G. D., & Moonen, E. J. G. (2005). Monitoring infrequent failures of high‐volume production processes. Quality and Reliability Engineering International, 21(5), 521-528.
Dogu, E., & Noor-ul-Amin, M. (2021). Monitoring exponentially distributed time between events data: self-starting perspective. Communications in Statistics-Simulation and Computation, 1-13.
Goh, T. N. (1987). A control chart for very high yield processes. Quality Assurance, 13(1), 18-22.
Guo, B., Yang, Y., & Castagliola, P. (2024). Optimal design of time-between-event control charts with parameter estimation. Quality Engineering, 1-12.
Hakimia, A., Farughi, H., Amiri, A., & Arkata, J. (2022).  Data Consumption Analysis by Two Ordinal Multivariate Control Charts. International Journal of Engineering, 35(11),2196-2204.
He, B., Xie, M., Goh, T. N., & Tsui, K. L. (2006). On control charts based on the generalized Poisson model. Quality Technology & Quantitative Management, 3(4), 383-400.
He, Y., Mi, K., & Wu, C. (2012). A New Statistical High‐Quality Process Monitoring Method: The Counted Number Between Omega‐Event Control Charts. Quality and Reliability Engineering International, 28(4), 427-436.
Hu, X., Castagliola, P., Zhong, J., Tang, A., & Qiao, Y. (2021). On the performance of the adaptive EWMA chart for monitoring time between events. Journal of Statistical Computation and Simulation, 91(6), 1175-1211.
Hu, X., Xia, F., Zhang, J., & Song, Z. (2024). Combined Shewhart–EWMA and Shewhart–CUSUM monitoring schemes for time between events. Quality and Reliability Engineering International, 40(6), 3352-3380.
Janada, K., Soltan, H., Hussein, M. S., & Abdel-Shafi, A. (2022). Angular Control Charts: A new perspective for monitoring reliability of multi-state systems. Computers & Industrial Engineering, 172, 108621.
Kumar, N., Rakitzis, A. C., Chakraborti, S., & Singh, T. (2024). Statistical design of ATS-unbiased charts with runs rules for monitoring exponential time between events. Communications in Statistics-Theory and Methods, 53(3), 815-833.
Lucas, J. M. (1985). Counted data CUSUM's. Technometrics, 27(2), 129-144.
Maleki, M. R., Ghashghaei, R., & Amiri, A. (2016). Simultaneous Monitoring of Multivariate Process Mean and Variability in the Presence of Measurement Error with Linearly Increasing Variance under Additive Covariate Model (RESEARCH NOTE). International Journal of Engineering, 29(4), 514-523.
Mirzaei Novin, M., & Amiri, A. (2023). Simultaneous monitoring of multivariate time between events and their magnitude using multivariate marked Hawkes point process. Quality Technology & Quantitative Management, 21(6), 1004-1024.
Niaz, A., Khan, M., & Ijaz, M. (2025). One‐Sided Modified EWMA Control Charts for Monitoring Time Between Events. Quality and Reliability Engineering International.
Pu, W., & Li, Y. (2023). Evaluating structural failure probability during aftershocks based on spatiotemporal simulation of the regional earthquake sequence. Engineering Structures, 275, 115267.
Qu, L., Wu, Z., Khoo, M. B., & Rahim, A. (2014). Time-between-event control charts for sampling inspection. Technometrics, 56(3), 336-346.
Rahali, D., Castagliola, P., Taleb, H., & Khoo, M. B. (2019). Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions. Quality Engineering, 31(2), 240-254.
Rahali, D., Castagliola, P., Taleb, H., & Khoo, M. B. C. (2021). Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data. Quality and Reliability Engineering International, 37(1), 219-241
Sanusi, R. A., Teh, S. Y., & Khoo, M. B. (2020). Simultaneous monitoring of magnitude and time-between-events data with a Max-EWMA control chart. Computers & Industrial Engineering, 142, 106378.
Shamstabar, Y., Shahriari, H., & Samimi, Y. (2021). Reliability monitoring of systems with cumulative shock-based deterioration process. Reliability Engineering & System Safety, 216, 107937.
Talib, A., Ali, S., & Shah, I. (2024). Max-EWMA chart for time and magnitude monitoring using generalized exponential distribution. Communications in Statistics - Simulation and Computation, 53(4), 1857–1872.
Vardeman, S., & Ray, D. O. (1985). Average run lengths for CUSUM schemes when observations are exponentially distributed. Technometrics, 27(2), 145-150.
Wu, Z., Khoo, M. B., Shu, L., & Jiang, W. (2009a). An np control chart for monitoring the mean of a variable based on an attribute inspection. International Journal of Production Economics, 121(1), 141-147.
Wu, Z., Jiao, J., & He, Z. (2009b). A control scheme for monitoring the frequency and magnitude of an event. International Journal of Production Research, 47(11), 2887-2902.
Xie, M., Goh, T. N., Kuralmani, V., & Kuralmani, V. (2002). Statistical models and control charts for high-quality processes. Springer Science & Business Media.
Zwetsloot, I. M., Mahmood, T., & Woodall, W. H. (2020). Multivariate time-between-events monitoring: An overview and some overlooked underlying complexities. Quality Engineering, 33(1), 13-25.
Zwetsloot, I. M., Mahmood, T., Taiwo, F. M., & Wang, Z. (2023). A real‐time monitoring approach for bivariate event data. Applied Stochastic Models in Business and Industry, 39(6), 789-817.