Optimization design of the EWMA and X-bar chart

Abstract

The design and optimization of Statistical process control (SPC) charts such as the Shewhart X-bar and the Exponential Weighted Moving Average Chart (EWMA) in order to achieve enhanced performance and high efficiency of its application in process quality control. It is accomplished by minimizing the loss function E which is related to the monetary loss due to poor quality product. The aim is to obtain an optimized sample size n for X-bar chart and parameter λ for EWMA chart, and sample interval h for both charts. Performance comparisons between the EWMA and Shewhart X-bar charts are conducted based on the minimized loss function. Numerical case examples will be used to illustrate the comparison and the applications of these optimized EWMA and Shewhart X-bar charts in production process scenarios.