Time-Between-Event Control Charts for Sampling Inspection

Time-between-events (TBE) charts or T charts have attracted increasing research interest in statistical process control (SPC). These charts monitor TBE or the time interval T between the events. Currently, almost all studies on T charts are focused on applications under 100% inspection. However, due to limitations in resources and working conditions, sampling inspection has to be adopted for many SPC applications, especially when testing is destructive and/or expensive. The operational characteristics of T charts under sampling inspection could be quite different from those under 100% inspection. Specifically, some highly efficient techniques or methods, such as sequential analysis, may be adopted for sampling inspection. This article studies four T charts for sampling inspection: (1) a Shewhart T chart; (2) a CUSUM T chart and its variable sample size version; (3) a SA T chart (the T chart using sequential analysis); and (4) a curtailed SA T chart. It is the first time that sequential analysis and curtailment technique are adopted for TBE control charts. It is found that these SA-type charts, especially the curtailed chart, are significantly more effective than the Shewhart T chart, CUSUM T chart, and any other charts in current literature. This article has supplementary material online.

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