The multi-objective economic statistical design of the p-chart: NSGA II approach

Abstract

A control chart is a crucially important tool in statistical process control that is essentially used to differentiate between assignable and chance causes of variation. With the advent of Six Sigma in the parlance of quality management, the control chart assumes more significance to hold the gain in the control phase after attaining process improvement in the improve phase. The sample size, sampling interval, and control limits’ multiplier are three important parameters required to design an effective as well as efficient control chart. Many approaches like economic design, statistical design, and economic statistical design of control charts have been studied by several researchers. All these approaches consider a single objective function. In this paper, we have proposed a multi-objective design of the p-chart, where we are minimizing both out-of-control Average Run Length ( ARL δ ) and the expected cost per cycle ( C E ). Non-dominated Sorting Genetic Algorithm II (NSGA II) is used to solve the proposed multi-objective model. The proposed approach is demonstrated with the help of two numerical examples and the corresponding results are found to be quite encouraging for minimizing both objectives in comparison to another pertinent model given in the literature. Sensitivity analysis has been carried out to give credence to the worth of the proposed approach.