On the Development of EWMA Control Chart for Inverse Maxwell Distribution

Abstract

Abstract Variations are usually present in every manufacturing process. Control charts are implemented to detect the assignable cause variations in a process. In this article, we design an exponentially weighted moving average (EWMA) chart under the assumption of inverse Maxwell distribution, namely inverse Maxwell EWMA (IMEWMA) chart. We have evaluated the performance of the proposed chart in terms of various run length (RL) properties, including average RL, standard deviation of RL, and median RL. To examine the overall functioning ability, we have estimated extra quadratic loss, relative average RL, and performance comparison index. We have also carried out comparative analysis of the proposed chart with the existing Shewhart-type chart for Maxwell distribution, V chart. We observed that the proposed IMEWMA chart performed better than the V chart to detect small and moderate shifts. The IMEWMA and the existing charts were applied to monitor the lifetime of car brake pads and survival time for breast cancer patients. This example also depicts the superiority of the proposed chart to its existing counterparts.