Simultaneous monitoring of magnitude and time-between-events data with a Max-EWMA control chart

Control charting techniques for monitoring the magnitude and frequency of an event are crucial in manufacturing and industrial activities. Several articles on monitoring the two quantities separately are available in the literature, however, a simultaneous monitoring of the magnitude and frequency of an event may be more time efficient. In this paper, we propose the maximum exponentially weighted moving average (Max-EWMA) control chart to simultaneously monitor the magnitude and frequency of an event. The Max-EWMA chart's statistic is based on the maximum of the absolute values of two EWMA statistics - one for controlling the magnitude and the other for the frequency of an event. In addition, the magnitude is assumed to follow a gamma distribution while the frequency is assumed to follow an exponential distribution. The objective of the proposed scheme is to enhance the speed for detecting shifts in the magnitude and/or frequency of an event. Overall, performance study indicates that the Max-EWMA chart outperforms its existing counterparts with the same objective of detecting small shifts in process parameters. It also competes strongly in detecting large shifts. Finally, we illustrate the application of the proposed chart with examples.