Control chart design for minimizing the proportion of defective units

Abstract

This article develops an algorithm for the optimization design of control charts. The design optimizes the sample size, sampling interval, and control limits of the chart 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 the MD chart. As with economic charts, the MD chart aims at reducing the quality cost. The design of this chart requires only limited number of specifications, which 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. A three-phase operational scenario for SPC (statistical process control) is adopted to design and implement the MD chart. Specifically, the process shift (e.g., mean shift, δ μ) is handled as a random variable by using a parametric or nonparametric approach to manipulate the sample data of δ μ acquired in the three-phase scenario. The results of the comparative studies show that the MD chart is significantly superior to the Shewhart control chart in overall performance. Although the MD chart is discussed in detail only for the X ¯ chart, the general idea can be applied to many other charts, such as CUSUM and EWMA charts.