Statistical Design of an Adaptive Synthetic (X)over-bar Control Chart with Run Rule on Service and Management Operation

An improved synthetic (X) over bar control chart based on hybrid adaptive scheme and run rule scheme is introduced to enhance the statistical performance of traditional synthetic (X) over bar control chart on service and management operation. The proposed scientific hybrid adaptive schemes consider both variable sampling interval and variable sample size scheme. The properties of the proposed chart are obtained using Markov chain approach. An extensive set of numerical results is presented to test the effectiveness of the proposed model in detecting small and moderate shifts in the process mean. The results show that the proposed chart is quicker than the standard synthetic (X) over bar chart and CUSUM chart in detecting small and moderate shifts in the process of service and management operation.