Control Charts for Quantile Function Values

Abstract

A control chart is proposed which monitors the conformance of a sample to an in-control distribution using the quantile or inverse cumulative distribution function. This method permits detecting changes in the distributional shape which may be undetected by control charts based on summary statistics. A vector of quantile function values is chosen which represents points where the in-control and out-of-control distributions differ most. These control charts are demonstrated on data from a packaging process where the in-control distribution is skewed and the out-of-control distributions which contain excessive overfill differ in shape.

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