Detecting outliers in complex profiles using a χ2control chart method

Abstract

The quality of products or manufacturing processes is sometimes characterized by profiles or functions. A method is proposed to identify outlier profiles among a set of complex profiles which are difficult to model with explicit functions. It treats profiles as vectors in high-dimension space and applies a χ2 control chart to identify outliers. This method is useful in Statistical Process Control (SPC) in two ways: (i) identifying outliers in SPC baseline data; and (ii) the on-line monitoring of profiles. The method does not require explicit expression of the function between the response and explanatory variables or fitting regression models. It is especially useful and sometimes the only option when profiles are very complex. Given a set of profiles (high-dimension vectors), the median of these vectors is derived. The variance among profiles is estimated by considering the pair-wise differences between profiles. A χ2 statistic is derived to compare each profile to the center vector. A simulation experiment and manufacturing data are used to illustrate applications of the method. Comparing it with the existing non-linear regression method shows that it has a better performance: it misidentifies fewer non-outlier profiles as outliers than the non-linear regression method, and misidentifies similarly small fractions of outlier profiles as non-outliers. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]

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