Dynamic VSI Max-EWMA control chart for joint monitoring of time-between-events and amplitude in high-quality manufacturing processes

Control charting methodologies for surveillance of an event frequency and amplitude are essential in manufacturing and industrial operations. There are some existing research works regarding the independent monitoring of the two values. Nevertheless, concurrently surveillance of an event's frequency and amplitude may prove to be more practical and effective. This study introduces the maximum exponentially weighted moving average (Max-EWMA) scheme with variable sampling interval (VSI) strategy (denoted as VSI Max-EWMA scheme) for the concurrent surveillance of both the frequency and amplitude of an event. The VSI strategy enables the VSI Max-EWMA scheme to adjust its sampling interval dynamically, switching between long and short intervals using the position of the current sample. Similar to the existing Max-EWMA scheme, the VSI MaxEWMA scheme's statistic corresponds to the maximum of the absolute values of two EWMA statistics, i.e., one for monitoring the frequency and another for tracking the amplitude of an event. Note that the frequency is expected to conform to an exponential distribution, whereas the amplitude is anticipated to adhere to a gamma distribution. The suggested approach aims to improve the speed of identifying changes in the event's frequency and/or amplitude. The performance analysis demonstrates that the VSI Max-EWMA scheme surpasses its existing counterparts in identifying minor and medium changes in the process based on the average time to signal (ATS) criterion. Lastly, we demonstrate the utilization of the suggested scheme by using integrated circuit chips dataset in the Electrical and Electronics industry, and demand and sales data of an automotive industry. For the integrated circuit chips dataset applied in this paper, the VSI Max-EMWA scheme detects its first OC signal at the 12.5-time units, which is quicker than the Max-EWMA scheme at 17-time units.