Use of Conditional False Alarm Metric in Statistical Process Monitoring

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.