Minimum Cost Multivariate Quality Control Tests

Abstract

An approximate expected cost model for the Hotelling T2 control chart is presented. This control chart is a multivariate analog of the X control chart. A method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the T2 chart. Numerical results are provided for several bivariate problems for various values of the cost coefficients. The model sensitivity to the cost coefficients, the shift parameter, the sample correlation coefficient, and the sample covariance matrix is discussed.

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