Variable sampling interval run sum X‾ chart with estimated process parameters

The X‾ type control chart is often evaluated by assuming the process parameters are known. However, the exact values of process parameters are hardly known and thus Phase-I dataset is needed to estimate them. In this paper, the performance of the variable sampling interval run sum X‾ chart with estimated process parameters is evaluated by using the performance measure of the average of the average time to signal (AATS) and the optimal design of the proposed chart in minimizing the out-of-control AATS is developed. The performance measure of the standard deviation of the average time to signal (SDATS) is then used to identify the number of Phase-I samples (w) needed to have an in-control AATS performance close to its known process parameter case. Results show that large w is needed to minimize the performance gap between known and unknown process parameters cases of the VSI RS X‾ chart