Optimal filter design approaches to statistical process control for autocorrelated processes

Statistical Process Control (SPC), and in particular control charting, is widely used to achieve and maintain control of various processes in manufacturing. A control chart is a graphical display that plots quality characteristics versus the sample number or the time line. Interest in effective implementation of control charts for autocorrelated processes has increased in recent years. However, because of the complexities involved, few systematic design approaches have thus far been developed. Many control charting methods can be viewed as the charting of the output of a linear filter applied to the process data. In this dissertation, we generalize the concept of linear filters for control charts and propose new control charting schemes, the general linear filter (GLF) and the 2nd-order linear filter, based on the generalization. In addition, their optimal design methodologies are developed, where the filter parameters are optimally selected to minimize the out-of-control Average Run Length (ARL) while constraining the in-control ARL to some desired value. The optimal linear filters are compared with other methods in terms of ARL performance, and a number of their interesting characteristics are discussed for various types of mean shifts (step, spike, sinusoidal) and various ARMA process models (i.i.d., AR(1), ARMA(1,1)). Also, in this work, a new discretization approach for substantially reducing the computational time and memory use for the Markov chain method of calculating the ARL is proposed. Finally, a gradient-based optimization strategy for searching optimal linear filters is illustrated

Cumulative sum quality control charts design and applications

Includes bibliographical references (pages 165-169).Classical Statistical Process Control Charts are essential in Statistical Control exercises and thus constantly obtained attention for quality improvements. However, the establishment of control charts requires large-sample data (say, no less than I 000 data points). On the other hand, we notice that the small-sample based Grey System Theory Approach is well-established and applied in many areas: social, economic, industrial, military and scientific research fields. In this research, the short time trend curve in terms of GM( I, I) model will be merged into Shewhart and CU SUM two-sided version control charts and establish Grey Predictive Shewhart Control chart and Grey Predictive CUSUM control chart. On the other hand the GM(2, I) model is briefly checked its of how accurate it could be as compared to GM( I, 1) model in control charts. Industrial process data collected from TBF Packaging Machine Company in Taiwan was analyzed in terms of these new developments as an illustrative example for grey quality control charts