A Multivariate Process Capability Index Based on the First Principal Component Only

Ingrid Tano · Kerstin Vännman

33 citations0/0 files storedQuality and Reliability Engineering International

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Advanced Statistical Process Monitoring Management and Optimization Techniques Fault Detection and Control Systems

Abstract

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. Copyright © 2012 John Wiley & Sons, Ltd.

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References

1952Quality-Control Handbook.2000Using principal component analysis in process performance for multivariate data 2006Encyclopedia and Handbook of Process Capability Indices 2009New capability indices for evaluating the performance of multivariate manufacturing processes 2005Quality Evaluation of a Manufactured Product with Multiple Characteristics

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