Median‐rate control chart for simultaneous monitoring of frequency and magnitude of events

Abstract

AbstractControl charts are one of the most important tools of statistical process control. Many control charts have been developed for the monitoring of time between events. However, there are situations for which magnitude of events is also important and needs to be monitored along with the time between them. In this case, simultaneous monitoring of both time between and magnitude of events can be very efficient in detecting process changes. Therefore, a single control chart, referred to as the median‐rate chart, is developed in this paper for simultaneous monitoring of magnitude and frequency of events. It is supposed that the magnitude and frequency of events are independent, and follow gamma and exponential distributions, respectively. The proposed chart is based on the ratio of magnitude and time between events and the median of these variables. The results of the performance evaluation represent that the median‐rate chart mostly outperforms the existing charts in detecting both small and large shifts of the process. We use the average time to signal for comparing the power of the control charts in detecting out‐of‐control conditions. Finally, some examples are illustrated to show the applicability of the proposed chart.