Economic-statistical design of control chart with runs rules for correlation within sample

Abstract

The economic-statistical design of charts with 2-of-2 and 2-of-3 runs rules for correlated data within a sample is developed in this study, in which the Markov chain approach is adopted to derive the statistical properties of the charts with runs rules. Lorenzen–Vance cost model is modified to determine the optimal design parameters and the generalized reduced gradient algorithm is used to solve the model. The results of the sensitivity analysis show that changing the value of correlation coefficient from low to high level increases the values of the control limit coefficient and the out-of-control average time to signal.

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