Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

Abstract

Control charts are one of the critical tools for process monitoring. Test statistics are computed as a function of sample means in control charts for monitoring the process mean. In this study, these functions are modeled by filters. These filters have essential properties in both time and frequency domains. In previous studies, only their properties in the time domain have been considered. Thus, the resulting filters have sub-optimal performance. This study investigates the optimal design of these filters for monitoring the process mean. The behavior of these filters is analyzed not only in the time domain but also in the frequency domain. Properties such as stability are considered in designing this filter. An optimization model is designed and solved using a Genetic Algorithm to minimize the Average Run Length. The proposed optimal filter is compared with other control charts using simulation studies. Results showed the high speed of the proposed filter in detecting shifts in the process mean. The proposed optimal filter is also used to monitor the oil price of the OPEC basket. The results showed that shifts were detected at the right time using the proposed optimal filter.