An adaptive chart for monitoring the process mean and variance

Traditionally, an X̄ chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive X̄ and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint X̄ and R charts with fixed or adaptive parameters, they are not reliable in identifying the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non‐central chi‐square statistic chart. This new chart is more effective than the adaptive X̄ and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects.