Monitoring Serially-Dependent Processes with Attribute Data

Abstract

Traditional methods of statistical process control (SPC) assume that observations of a quality characteristic are uncorrelated. This paper examines the case in which unacceptable variability in a product at one station in a production sequence will cause unacceptable variability in a product at the succeeding station. This serial dependence means that conventional SPC may be ineffective. For example, serially-dependent processes with attribute data may be nonstationary, demonstrating a geometric increase in the probability of occurence of a defect. This increase can be arrested by placing control points in the chain, with respect to the variability of the process at each work station. A control point is an inspection or correction station or both, that will re-establish the product attribute to a desirable level at that point in the sequence. Some of the resulting segments will contain stations with such low probability of defect that a correlated effect over an abbreviated segment may behave according to distributions that can be controlled by conventional SPC methods. Other segments may magnify short trends to create out-of-control conditions. These segments can be controlled by regression control. This paper develops a control system that maintains stability of serially-dependent processes irrespective of the number of stations or basic defect rates of the individual work stations in the sequence.

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