RUN-LENGTH DISTRIBUTION FOR CONTROL CHARTS WITH SUPPLEMENTARY RUNS RULES USING FINITE MARKOV CHAIN EMBEDDING

초록

The Shewhart control chart is effective for detecting mid-to-large shifts but is less sensitive to small shifts. Supplementary runs rules(e.g., the Western Electric rules) are integrated to enhance model performance, the finite Markov chain embedding method is applied to calculate the run-length distribution accurately. This analysis reveals significant skewness in the distribution, highlighting the limitations of solely relying on the average run-length (ARL). For a more complete understanding of the chart performance, this work presents quartile values and the standard deviation of the run-length, complementing the ARL by capturing detection-time variability. This study enhances the efficiency of calculations using the Finite Markov Chain Embedding (FMCE) method and derives the probability mass function differently by considering a recursive scheme.

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