Redesigning the Joint SPRT Mean and Dispersion Control Chart Based on Mismatched In-control Performances

In most quality control practices, the mean control chart is used in conjunction with the dispersion control chart to maintain the stability of a production process. Existing literature has suggested setting the in-control average run length (ARL <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> ) of the mean chart and the dispersion chart to be equal. While such designs have the advantage of convenience, it is often unrealistic to assume that the mean and dispersion charts will share a common sensitivity, since mean shifts and variance shifts may occur with different probabilities in practice. In this paper, we propose a mismatched in-control performances strategy for designing the joint sequential probability ratio test (SPRT) mean and dispersion chart. We also develop new optimization designs for the joint SPRT scheme. Results show that the mismatched in-control performances strategy effectively boosts the detection sensitivity of the joint SPRT scheme towards mean shifts alone or variance shifts alone. It is also revealed that the mismatched joint SPRT scheme with a larger ARL on the dispersion chart performs better than the traditional matched joint SPRT scheme for a wide range of process shifts.