A simple categorical chart for detecting location shifts with ordinal information

Abstract

Traditional control charts for monitoring attribute data usually neglect the order among the attribute levels, such as good, marginal and bad, of a categorical factor. Such order may be reflected by an underlying continuous variable, which determines the level of the categorical factor by classifying it according to some thresholds in the latent continuous scale. This paper exploits this ordinal information and proposes a control chart for detecting location shifts in the latent variable based on merely the attribute level counts, regardless of the continuous values of the latent variable. The proposed ordinal chart is very simple to construct and enjoys the same setting as conventional categorical charts. Numerical simulations demonstrate the superiority of this simple ordinal categorical chart.

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