Max control chart with adaptive sample sizes for jointly monitoring process mean and standard deviation

This paper develops the two‐state and three‐state adaptive sample size control schemes based on the Max chart to simultaneously monitor the process mean and standard deviation. Since the Max chart is a single variables control chart where only one plotting statistic is needed, the design and operation of adaptive sample size schemes for this chart will be simpler than those for the joint [Xmacr ] and S charts. Three types of processes including on‐target initial, off‐target initial and steady‐state conditions are considered to evaluate the chart performance. The results of this study show that both two‐state and three‐state schemes are more efficient than the conventional non‐adaptive joint [Xmacr ] and S charts. The three‐state procedure is only slightly better than the two‐state scheme, and the most dramatic improvement occurs when the two‐state scheme is compared with the non‐adaptive joint [Xmacr ] and S charts. Moreover, with the ease of implementation, the two‐state scheme is likely adequate in most practical applications.