Monitoring and performance analysis of regression profiles

There are many cases in industrial and non-industrial sections where the quality characteristics are in the form of profiles. Profile monitoring is a relatively new set of techniques in statistical quality control that is used in situations where the state of product or process is presented by regression models. In the past few years, most research in the field of profile monitoring has mainly focused on the use of effective statistical charting methods, study of more general shapes of profiles, and the effects of violations of assumptions in profile monitoring. Despite several research on the application of artificial neural networks to statistical quality control, no research has investigated the application of neural networks in monitoring profiles. Likewise, there is no research in the literature on the process capability analysis in profile processes. The process capability analysis is to evaluate the ability of a process to meet the customer/engineering specifications and must be done in Phase I of profile monitoring. In a review study on profile monitoring, Woodall (2007) pointed out the importance of process capability analysis in profiles.

In this research, we use artificial neural networks (ANN) to detect and classify shifts in linear profiles. Three monitoring methods based on ANN are developed to monitor linear profiles in Phase II. We compare the results for different shift scenarios with existing methods in linear profile monitoring and discuss the results.

Furthermore, in this thesis, we evaluate the estimation of process capability indices (PCIs) in linear profiles. We propose a method based on the relationship between proportions of non-conformance and the process capability indices in the profile process. In most existing profile monitoring methods in the literature, it is assumed that the profile design points are deterministic (fixed) so they are unchanged from one profile to another one. In this research, we investigate the estimation of the PCI in normal linear profiles for different scenarios of deterministic and arbitrary (random) data acquisition schemes as well as fixed or linear functional specification limits. We apply the proposed method in estimating the PCI in a yogurt production process.

This thesis also focuses on the investigation of the process capability analysis in profiles with non-normal error terms. In this study, we review the methods for estimating PCI in non-normal data and carry out a comprehensive comparison study to evaluate the performance of these methods. Then these methods are applied in the leukocyte filtering process to evaluate the PCI with effect of non-normality in a blood service section. In addition, we develop a new method based on neural networks to estimate the parameters of the Burr XII distribution, which is required in some of the PCI estimation methods with non-normal environments.

Finally, in this research we propose five methods to estimate process capability index in profiles where residuals follow non-normal distributions. In a comparison study using Monte Carlo simulations we evaluate the performance of the proposed methods in terms of their precision and accuracy. We provide conclusions and recommendation for the future research at the end.