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Comparing Confidence Intervals for Multivariate Process capability Indices
University West, Department of Engineering Science, Division of Computer, Electrical and Surveying Engineering. (PTW)ORCID iD: 0000-0002-2965-488X
Umeå universitet, Umeå, Sverige.
2012 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 28, no 4, p. 481-495Article in journal (Refereed) Published
Abstract [en]

Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index Cp. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way. 

Place, publisher, year, edition, pages
Wiley online library , 2012. Vol. 28, no 4, p. 481-495
Keywords [en]
multivariate process capability index lower confidence bound multivariate normal distribution
National Category
Probability Theory and Statistics
Research subject
ENGINEERING, Mathematics; Production Technology
Identifiers
URN: urn:nbn:se:hv:diva-3775DOI: 10.1002/qre.1250ISI: 000304152600011OAI: oai:DiVA.org:hv-3775DiVA, id: diva2:447631
Available from: 2011-10-12 Created: 2011-10-12 Last updated: 2018-04-10Bibliographically approved
In thesis
1. Contributions to multivariate process capability indices
Open this publication in new window or tab >>Contributions to multivariate process capability indices
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Luelå: , 2012. p. 36
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
National Category
Mathematics
Research subject
ENGINEERING, Manufacturing and materials engineering
Identifiers
urn:nbn:se:hv:diva-4456 (URN)9789174393989 (ISBN)
Available from: 2012-06-28 Created: 2012-06-26 Last updated: 2012-06-28Bibliographically approved

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Tano, Ingrid

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