Development and evaluation of the control charts for variables

Abstract

In quality control (QC), control chart is one of the most effective tools to monitor the process and ensure the product quality. It is a powerful Statistical Process Control (SPC) method to make quick response when quality problems occur in order to avoid serious economic loss. The first objective of this PhD project is to develop new SPC techniques, for which several highly effective control charts for variables have been proposed and carefully investigated. The second task is to provide a systematic performance comparison among all typical control charts for variables including the Shewhart chart, Cumulative Sum (CUSUM) chart and Sequential Probability Ratio Test (SPRT) chart.

These studies are conducted in two phases. The first phase presents the development of the control charts for monitoring process mean. The Syn- , optimal SPRT and VSI (Variable Sampling Interval) SPRT charts have been developed in Chapter 3. A systematic study has also been conducted to compare the effectiveness and robustness of nine typical control charts for monitoring the mean of variables in Chapter 4. The nine charts are categorized into three types (the type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and fully-adaptive (FA) version). A design table has been made to facilitate the users to select a chart by taking into considerations of both performance and simplicity of the charts, as well as the probability distribution of the mean shift δµ of the process.

The second phase presents the development of the control charts for monitoring both process mean and variance. The VSSI (Variable Sample Size and Sampling Interval) CUSUM and ABS (Absolute) SPRT charts have been developed in Chapter 5. This phase also studies the overall performance of nine typical control charts for monitoring process mean and variance in a quantitative and analytical manner in Chapter 6.

A general model for the optimal designs of the control charts is adopted throughout this thesis. In this model, Average Extra Quadratic Loss (AEQL) is used as the objective function, in-control Average Time to Signal (ATS0) and inspection rate (R) are the constraints. It is expected that the development of the new charts and the systematic comparative studies carried out in this thesis will make useful contribution to the literature and practice of quality engineering.