Contributions to multivariate process capability indices
Sammanfattning: The work presented in this thesis considers multivariate process capability indices (MPCIs) with focus on confidence intervals and tests for MPCIs. It also includes a case study, where multivariate statistical analysis and MPCIs are applied to data from a thermal spraying process at Volvo Aero Corporation. A process capability index measures the ability of a process to satisfy customers’ demands. Since the knowledge about the process performance is based on a random sample, it is important to be able to handle the uncertainty this implies. If the uncertainty is not dealt with and the estimated index is used directly without considering, e.g. a confidence interval, an erroneous conclusion may be drawn about the process capability.The thesis consists of a summary and of three papers, one of which has been presented at an international conference, one has been accepted for publication in an international journal, and the third has been submitted for publication.In Paper I, multivariate statistical analysis is used for screening and tentative model building to describe the relationship between the porosity and the heat conductivity in the thermal spraying process. Object-oriented finite element analysis (OOF) is subsequently used for verification of the statistical model. The new approach functions well and confirms the findings from the statistical model.Paper II reviews and compares four different MPCIs with confidence intervals, requiring multivariate normal distribution. MPCIs are needed when the quality characteristic of interest is multivariate, i.e. when the quality characteristic consists of several correlated variables. The review shows that more research is needed to obtain an MPCI with a confidence interval or a test that works properly. In particular, it is required that a stated value of the MPCI at least limits the probability of non-conformance in a known way. A drawback is also elucidated with existing MPCIs based on principal component analysis.Paper III presents some method development with the purpose of meeting the deficiencies identified in Paper II. A new index together with a confidence interval and a decision procedure is developed that converts a multivariate situation into a familiar univariate situation. Well-known statistical theory for univariate process capability indices can then be used. Properties, like significance level and power, of the pro¬posed deci¬sion procedure is evaluated through a simulation study in the two-dimen¬sional case. A comparative simulation study between our new MPCI and an MPCI pre¬viously suggested in the literature is also done. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further.
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