The Conditional In-Control Performance of Self-Starting Control Charts

The recommended size of the Phase I data set used to estimate the in-control parameters has been discussed many times in the process monitoring literature. Collecting baseline data, however, can be difficult or slow in some applications. Such issues have resulted in the development of self-starting control charts that allow charting early, near the start of data collection. In our article, we use the average of the in-control average run length (AARL) and the standard deviation of the in-control average run length (SDARL) to assess the in-control run length performance of self-starting charts conditioned on the preliminary data used. This approach accounts for practitioner-to-practitioner variability in the in-control average run length (ARL) of self-starting charts, which has not been considered previously. We found that there was a significant amount of variation in the in-control ARL values obtained by practitioners due to the sampling variation of the initial estimators of the in-control parameters. The amount of variation was surprisingly low, however, compared to that resulting from the use of standard Phase I sampling and estimation.