Contributions to process capability indices and plots

This thesis presents contributions within the field of process capability analysis. Process capability analysis deals with how to assess the capability of processes. Based on process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices and process capability plots. The thesis consists of six papers and a summary. The summary gives a background to the research area, a short overview of the six papers, and some suggestions for future research. The thesis summary also consists of some new results, not presented in any of the appended papers. In paper I, the frequency and use of process capability analysis, together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, and what is needed to increase the use. In papers II-III we generalize the ideas with process capability plots and propose two graphical methods, for deeming a process capable at a given significance level, when the studied quality characteristic is assumed to be normally distributed. In paper II we derive estimated process capability plots for the case when the specification interval is one-sided. In paper III we derive elliptical safety region plots for the process capability index Cpk and its one-sided correspondences. The proposed graphical methods are helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In papers IV-VI we propose a new class of process capability indices designed for the situation with an upper specification limit, a target value zero, and where the studied quality characteristic has a skewed, zero-bound distribution with a long tail towards large values. The proposed class of indices is simple and possesses properties desirable for process capability indices. The results in papers IV-VI are also valid for the situation with a target value, not equal to zero but equal to a natural lower limit of the quality characteristic. Three estimators of the proposed class of indices are studied and the asymptotic distributions of these estimators are derived. We also consider decision procedures, based on the estimated indices, suitable for deeming the process capability at a given significance level. The new results in the summary combines the ideas from paper II with the results in papers IV-VI and a graphical method for the class of indices proposed in IV-VI are derived.