Statistical process monitoring for non-iid processes

Monitoring non-iid processes and fault diagnosis for root cause determination are very useful and challenging tasks for various manufacturing process quality control applications. In this thesis, several fundamental issues of these tasks have been studied and the major contributions are summarized as follows: (1) An SPC monitoring system using a Haar transform is developed by integrating conventional SPC charts and the Haar transforms. This SPC monitoring system utilizes the Haar transform as a feature extraction tool, which dramatically reduces the dimensionality of monitoring problems. This SPC monitoring system provides the capability of automatically detecting the mean shifts in a class of non-iid processes in which the observations are non-iid within a sample and joint-iid among samples. A real-world example of sheet metal stamping tonnage signal monitoring is provided to demonstrate the effectiveness of the developed SPC monitoring system. (2) A G-Haar transform is proposed to overcome some constraints of the Haar transform. The original contribution of this G-Haar transform is that it allows the number of observations to be any positive integer, which substantially facilitates the use of the conventional Haar transform. This G-Haar transform is normal and orthogonal. G-Haar coefficients have very clear physical interpretations and they can be customized so as to be very sensitive to the process faults. This has been demonstrated in the SPC monitoring system. In addition, the G-Haar transform provides a general framework in the family of Haar transforms. (3) A robustness analysis of SPC for autocorrelated data is studied in this research. The effect of parameter estimation uncertainty on the monitoring performance is analyzed for ARMA(1,1) and AR(2). The upper and lower bounds of ARL are developed with consideration of the modeling uncertainty, which provides a criterion of determining whether the model-based monitoring should be used given a specific parameter estimation uncertainty and the sample size. Sample-size design maps for ARMA(1,1) and AR(2) models are generated based on the analytical results for different required robustness index and meanshift magnitudes. As a result, a robust monitoring approach under parameter estimation uncertainty is further proposed for SPC for autocorrelated process monitoring.