| The use of Statistical Process Control (SPC) techniques to monitor production processes for quality improvement has gained widespread acceptance in industry. Various statistical control charts to monitor the process mean and variance are developed under the assumption that the process data is statistically independent. However, serial correlation exhibits in almost all industrial processes, continuous as well as discrete, especially in batch production processes. It is known that traditional control charts are poor for monitoring the mean level when the process is autocorrelated (Harris and Ross, 1991; Alwan, 1992).; Several types of SPC control chart have been developed for monitoring autocorrelated processes. Among them, the Special Cause Chart (SCC) and the EWMA chart for stationary process (EWMAST) are the two major types of control charts that have received considerable investigations. However, it is found that no chart can uniformly outperform the other for any situation studied, and no explanation has been given for the design of these control charts. In the thesis, a new family of charting schemes, Autoregressive Moving-Average (ARMA) charts, is proposed to monitor the mean of autocorrelated processes. The ARMA chart integrates conventional control charts such as the SCC and EWMAST charts into a unified correlation-based framework. Following a simulation study, it is shown that the ARMA chart is competitive to the optimal EWMA chart when the observations are identically independent, and better than other charts when observations are autocorrelated. Learning from the experience in Automatic Process Control (APC) practices, an ad hoc heuristic algorithm is developed for designing efficient ARMA chart based on the specific autocorrelated process. Meanwhile, the theoretical properties of the general ARMA charts are discussed comparing with conventional charts. Furthermore, an engineering-driven control chart, the Proportional-Integral-Derivative (PID) control chart which is a special class of higher order ARMA chart, is also studied. The PID chart is re-viewed as a transformation algorithm resulting from the output of the so-called PID controller applied to the system, and thus can be understood and used easily by control engineers in practice.; Although APC techniques such as feedback control schemes have been widely used to reduce common cause variations/autocorrelations in the production process, special cause variations may still happen. Because of the APC scheme employed, the nature of the special cause variation becomes different from that when no APC scheme is employed, and makes it difficult to be detected by conventional control charts. The ARMA chart, as well as the PID chart, can easily be designed to incorporate with the APC controller for monitoring the APC-controlled production process. Importantly, based on an economic model of the APC-controlled process, the commonly used criterion, Average Run Length (ARL), is found to be insufficient to evaluate the performance of control charts in the integrated APC and SPC environment. A new economic criterion, Average Quality Cost (AQC), is proposed for the design of appropriate control charts for monitoring production outputs from a Minimum Mean Square Error (MMSE) control scheme, and compared with the ARL criterion. The AQC criterion takes into consideration of the dynamic mean of the output as well as the run length distribution of the associated control chart, thus provides more information of the process than the ARL criterion. At last, several further research issues are discussed for the application and study of the new chart. |
