Advances in Cautious Parameter Learning for Statistical Process Control Models with Guaranteed In-Control Performance

This dissertation concerns itself with the advancement of Guaranteed In Control Performance and Cautious Learning procedures in Statistical Process Control, a research field that focuses on sequential hypothesis testing procedures to assess process stability. Central to the field is the control chart, a tool that provides quality practitioners in various settings with an uncomplicated method to interpret the hypothesis test’s results. The control chart relies on an underlying statistical model that has to be estimated from a data sample which is generally obtained in a study of the process of interest’s stable-state behavior, i.e. the quality variable’s function and its moments. However, when the model is estimated from a small initial sample, which is in some settings unavoidable for economical and practical reasons, estimation errors and practitioner-to-practitioner variation result in a high variability in the control chart’s average performance. This in turn results in unreliable signaling behavior that erodes the control chart’s usefulness. Recently introduced Guaranteed In-Control Performance and Cautious Learning procedures were shown to mitigate performance issues due to poor model fit. The first research paper concerns itself with the evolution of univariate learning control charts, starting with the history of the field, followed by its evolution and state-of-the-art. The second research paper extends the recently introduced Guaranteed In-Control Performance and Cautious Learning procedures for control of a quality variable’s mean to the joint monitoring of mean and variance. In this study a joint mean and variance cumulative sum scheme is introduced and its performance under different learning procedures evaluated. Based on the study’s results design guidelines for practitioners are put forward along with a calibration algorithm to address the complex issue of balancing the individual control chart’s sensitivity. The third research paper addresses the steadiness of the Guaranteed In-Control Performance as the control chart’s underlying model is adapted. It is demonstrated that the design of the cautious learning procedures in preceding studies result in a gradual loss in sensitivity and consequently departure from specification. An alternative design is derived and recommendations for practical application are put forward, including a calibration algorithm. Ultimately, this research addresses two gaps in the SPC literature. Firstly, it provides practitioners and researchers with an extensive review of learning models that is currently missing. Secondly, it supplies improved tools to address the estimation error problem that afflicts SPC models in Phase II when only limited Phase I data is available, thereby advancing the SPC body of knowledge.