Process Capability Analysis with Focus on Indices for One- sided Specification Limits

In this thesis some aspects of process capability analysis are considered. Process capability analysis deals with how to assess the capability of manufacturing processes. Based on the 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 in the situation when the specification limits are one-sided. The thesis consists of a summary and three papers, of which one is already published in an international journal. The summary gives a background to the research area, a short overview of the three papers, and some suggestions for future research. 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, if there are differences in use that can be related to organisational types and what will be needed to increase the use. One conclusion drawn from the results is that the students employed in the Swedish industrial sector witness a modest use of these statistical methods and use in other sectors hiring the alumni is uncommon. In Paper II we present a graphical method useful when doing capability analysis having one-sided specification limits. This is an extension of the process capability plots previously developed for two-sided specification intervals. Under the assumption of normality we suggest estimated process capability plots to be used to assess process capability at a given significance level. The presented graphical approach is helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In Paper III the situation with non-negative process data having a skew distribution with a long tail towards large values are considered, when an upper specification limit only exists and the target value is 0. No proper indices exist for this specific situation, which is common in practice. We contribute to this area by proposing a new class of indices, ( , ) MA C v , designed for skew, zero-bound distributions when an upper specification only exists and the target value is 0. This new class of indices is simple and possesses properties desirable for process capability indices. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore, we consider decision procedures, based on the estimated indices, suitable for deeming the process capability or not.