Using Runs Rules to Monitor an Attribute Chart for a Markov Process

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Quality Technology and Quantitative Management






For some repetitive production processes, the quality measure taken on the output is an attribute variable. An attribute variable classifies each output item into one of a countable set of categories. One of the simplest and most commonly used attribute variables is the one that classifies an item as either "conforming" or "nonconforming." A tool used with a considerable amount of success in industry for monitoring the quality of a production process is the quality control chart. In this paper, a sequence of random variables, Xi , i = 1,2,… , is used to classify an item as conforming or nonconforming under a stationary Markov chain model and under 100% sequential sampling. The sequence of random variables to be plotted on the control chart is Yi , i = 1,2,… , where Y1 counts the number of conforming items before the first nonconforming item and Yi , i = 2,3,… counts the number of conforming items between the (i-1)th and the ith nonconforming items. In the literature, Yi is called the CRL (Conforming Run Length). The contribution of this paper to the literature is to present runs rules for an attribute control chart of this type. The efficiency of these charts is evaluated using the average run length (ARL) of the charts. The supplemental runs rules that are presented are two out of three values of Yi , i 1,2, falling below determined lower limits, four out of five values of Yi , i =1,2,…falling below determined lower limits, and eight out of eight values of Yi , i =1,2,… falling below determined lower limits.