A Program to Evaluate the Run Length Distribution of a Shewhart Control Chart with Supplementary Runs Rules

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Abstract
A FORTRAN program is given for evaluating the properties of the run length distribution of a Shewhart quality control chart with supplementary runs rules. The program has two parts. The first part (Part 1) of the program determines the minimal set of states and the next-state transitions for a Markov chain representation. This part is an implementation of the technique developed by the authors in an earlier paper. The results from Part 1 contain information that is necessary to obtain in the second part (Part 2) the transition matrix of the Markov chain. Part 1 can be used for any type of Shewhart chart that has been supplemented with runs rules, whereas Part 2 is only applicable to the Shewhart X̄ chart. Part 2 uses the results from Part 1 to obtain the cumulative distribution function of the run length, the average run length, and the standard deviation of the run length for a specified standardized shift in the mean.