EWMA control chart that minimizes the numbers of defectives for out-of-control cases

This article develops an algorithm for the optimization design of Exponentially Weighted Moving Average (EWMA) control charts. The design algorithm adjusts the sample size, sampling interval and control limits of the chart in an optimal manner in order to minimize the mean number of defective units (denoted as MD) produced per out-of-control case. The optimal chart is therefore named as the MD-EWMA chart. The probability distribution of the random process shifts (e.g. mean shift) is taken into account and is modeled by a Rayleigh distribution based on the sample data acquired during the operation of the control chart. Unlike the economic control chart designs, the design of the MD-EWMA chart only requires limited number of specifications that can be easily determined. The design of the proposed MD-EWMA chart is illustrated through an example.