Design of EWMA control chart for minimizing the proportion of defective units

Abstract

PurposeThe exponentially weighted moving average (EWMA) control charts are widely used in industries for monitoring small and moderate process shifts. The purpose of this paper is to develop an algorithm for the optimization design of the EWMA chart (known as MD‐EWMA chart).Design/methodology/approachThe design algorithm adjusts the sample size n, sampling interval h, lower and upper control limits LCL and UCL, and the EWMA weight factor λ 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 probability distribution of the random process shift (e.g. mean shift δ) is taken into account that may be modeled by a Rayleigh distribution based on the sample data acquired during the operation of the control chart.FindingsThe results of the comparison studies and an example show that the proposed MD‐EWMA chart is significantly superior to the Shewhart‐type MD‐X¯ chart and the other EWMA charts in terms of the overall mean defective MD.Originality/valueAs the economic charts, the proposed MD‐EWMA chart aims at reducing the quality cost. But the design of this chart only requires limited number of specifications that can be easily determined. Consequently, the MD chart provides the control chart designers with an alternative choice between the statistical design and the economic design. Specifically, the mean shift δ is handled as a random variable by using a parametric or nonparametric approach to manipulate the sample data of δ acquired during the operation of the control chart. The MD counts the number of defective units produced per out of control case; so the design of control chart based on MD is more realistic from a practical viewpoint. In addition, the design of MD‐EWMA chart combines forecasting with controlling methods of quality management.