Performance measures of discrete and continuous time-between-events control charts

An increasing number of applications in the chemical industry involve measuring nonconforming items, particularly in high-purity processes or high-yield processes. Dedicated monitoring tools such as the time-between-events (TBE) control charts have been developed for both discrete time (CCC-charts) and continuous time (t_r-charts) for detecting any shifts in the process defect rate. However, most common performance metrics used in literature are not always appropriate and may not suffice to describe the efficiency of a monitoring system. The definition of conditional performance measures described in the literature is extended to TBE charts. These metrics are computed for Shewhart-type TBE charts with run rules and used to compare these charts at different aggregation levels.