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A multivariate process capability index based on the first principal component only
Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden. (Department of Engineering Science, University West, Trollhättan, Sweden)
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. (Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden and Department of Engineering Science, University West, Trollhättan, Sweden)
2013 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 29, no 7, 987-1003 p.Article in journal (Refereed) Published
Abstract [en]

Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well-known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non-conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two-dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further.

Place, publisher, year, edition, pages
John Wiley & Sons, 2013. Vol. 29, no 7, 987-1003 p.
Keyword [en]
multivariate process capability index, multivariate normal distribution, transformed variable, principal component analysis, Cp, significance level, power
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-59854DOI: 10.1002/qre.1451ISI: 000333581600005OAI: diva2:556944
Available from: 2012-09-26 Created: 2012-09-26 Last updated: 2014-06-05Bibliographically approved

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