Abstract
The conditional false alarm rate (CFAR) at a particular time is the probability of a false alarm for an assumed in-control process at that time conditional on no previous false alarm. Only the Shewhart control chart designed with known in-control parameters, or conditioned on the estimated parameters, has a constant conditional false alarm rate. Other types of charts, however, can have their control limits determined in order to have any desired pattern of CFARs. The important advantage of the use of this CFAR metric is when sample sizes, population sizes or other covariate information affecting chart performance vary over time. In these cases, the control limit at a particular time can be obtained through control of the CFAR value after the corresponding covariate value is known. This allows one to control the in-control performance of the chart without the need to model or forecast the covariate values. The approach is illustrated using the risk-adjusted Bernoulli cumulative sum (CUSUM) chart.
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References
Aminnayeri, M., & Sogandi, F. (2016). A risk adjusted self-starting Bernoulli CUSUM control chart with dynamic probability control limits. AUT Journal of Modeling and Simulation, 48(2), 103–110.
Aytaçoǧlu B., Woodall, W. H. (2020). Dynamic probability control limits for CUSUM charts for monitoring proportions with time-varying sample sizes. Quality and Reliability Engineering International, 36, 592–603.
Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448–459.
Du, L., & Zou, C. (2018). On-line control of false discovery rates for multiple datastreams. Journal of Statistical Planning and Inference, 194, 1–14.
Hawkins, D. M., & Deng, Q. (2010). A nonparametric change-point control chart. Journal of Quality Technology, 42(2), 165–173.
Hawkins, D. M., & Zamba, K. (2005a). A change-point model for a shift in variance. Journal of Quality Technology, 37(1), 21–31.
Hawkins, D. M., & Zamba, K. (2005b). Statistical process control for shifts in mean or variance using a changepoint formulation. Technometrics, 47(2), 164–173.
Hawkins, D. M., Qiu, P., & Kang, C. W. (2003). The changepoint model for statistical process control. Journal of Quality Technology, 35(4), 355–366.
Holland, M. D., & Hawkins, D. M. (2014). A control chart based on a nonparametric multivariate change-point model. Journal of Quality Technology, 46(1), 63–77.
Huang, W., Shu, L., Woodall, W. H., & Tsui, K. L. (2016). CUSUM procedures with probability control limits for monitoring processes with variable sample sizes. IIE Transactions, 48(8), 759–771.
Margavio, T. M., Conerly, M. D., Woodall, W. H., & Drake, L. G. (1995). Alarm rates for quality control charts. Statistics and Probability Letters, 24(3), 219–224.
Morais, M. C., & Pacheco, A. (2012). A note on the aging properties of the run length of Markov-type control charts. Sequential Analysis, 31(1), 88–98.
Nishina, K., & Nishiyuki, S. (2003). False alarm probability function of CUSUM charts. Economic Quality Control, 18(1), 101–112.
Nishina, K., Kuzuya, K., & Ishii, N. (2006). Reconsidering control charts in Japan. Frontiers in statistical quality control 8 (pp. 136–150). Springer.
Shen, X., Zou, C., Jiang, W., & Tsung, F. (2013). Monitoring Poisson count data with probability control limits when sample sizes are time varying. Naval Research Logistics (NRL), 60(8), 625–636.
Shen, X., Tsui, K. L., Zou, C., & Woodall, W. H. (2016). Self-starting monitoring scheme for Poisson count data with varying population sizes. Technometrics, 58(4), 460–471.
Sogandi, F., Aminnayeri, M., Mohammadpour, A., & Amiri, A. (2019). Risk-adjusted Bernoulli chart in multi-stage healthcare processes based on state-space model with a latent risk variable and dynamic probability control limits. Computers and Industrial Engineering, 130, 699–713.
Steiner, S. H., Cook, R. J., Farewell, V. T., & Treasure, T. (2000). Monitoring surgical performance using risk-adjusted cumulative sum charts. Biostatistics, 1(4), 441–452.
Tang, X., Gan, F. F., & Zhang, L. (2015). Risk-adjusted cumulative sum charting procedure based on multiresponses. Journal of the American Statistical Association, 110(509), 16–26.
Woodall, W. H. (2007). Current research on profile monitoring. Production, 17(3), 420–425.
Woodall, W. H., & Faltin, F. (2019). Rethinking control chart design and evaluation. Quality Engineering, 31(4), 596–605.
Woodall, W. H., & Montgomery, D. C. (1999). Research issues and ideas in statistical process control. Journal of Quality Technology, 31(4), 376–386.
Yang, W., Zou, C., & Wang, Z. (2017). Nonparametric profile monitoring using dynamic probability control limits. Quality and Reliability Engineering International, 33(5), 1131–1142.
Zamba, K., & Hawkins, D. M. (2006). A multivariate change-point model for statistical process control. Technometrics, 48(4), 539–549.
Zamba, K., & Hawkins, D. M. (2009). A multivariate change-point model for change in mean vector and/or covariance structure. Journal of Quality Technology, 41(3), 285–303.
Zhang, X., & Woodall, W. H. (2015). Dynamic probability control limits for risk-adjusted Bernoulli CUSUM charts. Statistics in Medicine, 34(25), 3336–3348.
Zhang, X., & Woodall, W. H. (2017a). Dynamic probability control limits for lower and two-sided risk-adjusted Bernoulli CUSUM charts. Quality and Reliability Engineering International, 33(3), 607–616.
Zhang, X., & Woodall, W. H. (2017b). Reduction of the effect of estimation error on in-control performance for risk-adjusted Bernoulli CUSUM chart with dynamic probability control limits. Quality and Reliability Engineering International, 33(2), 381–386.
Zhang, X., Loda, J. B., & Woodall, W. H. (2017). Dynamic probability control limits for risk-adjusted CUSUM charts based on multiresponses. Statistics in Medicine, 36(16), 2547–2558.
Zhou, C., Zou, C., Zhang, Y., & Wang, Z. (2009). Nonparametric control chart based on change-point model. Statistical Papers, 50(1), 13–28.
Zou, C., & Tsung, F. (2010). Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology, 42(2), 174–196.
Zou, C., Zhang, Y., & Wang, Z. (2006). A control chart based on a change-point model for monitoring linear profiles. IIE Transactions, 38(12), 1093–1103.
Zou, C., Qiu, P., & Hawkins, D. (2009). Nonparametric control chart for monitoring profiles using change point formulation and adaptive smoothing. Statistica Sinica, 19, 1337–1357.
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The authors are grateful to an anonymous referee for insightful comments that have improved the article.
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Driscoll, A.R., Woodall, W.H., Zou, C. (2021). Use of Conditional False Alarm Metric in Statistical Process Monitoring. In: Knoth, S., Schmid, W. (eds) Frontiers in Statistical Quality Control 13. ISQC 2019. Frontiers in Statistical Quality Control. Springer, Cham. https://doi.org/10.1007/978-3-030-67856-2_1
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