Economic Design of Exponentially Weighted Moving Average Control Chart Based on Measurement Error Using Genetic Algorithm

Control charts are one of the most well‐known statistical process control tools used for quick detecting changes in the process. One of their types is exponentially weighted moving average control chart. To apply them economically requires determination of corresponding parameters. Because the sampling is used to ensure process stability, the presence of measurement error in control charts seems avoidable. The presence of measurement error in control charts reduces their performance and delays quick reaction to changes. To reduce this effect, taking multiple measurements on quality characteristic of each unit is made. Previous researches do not consider the effect of measurement error on the cost function of control charts. In this paper, considering measurement error and taking multiple measurements, as well as linear and Taguchi loss functions for poor quality products, the cost function of exponentially weighted moving average control chart is modeled. For the proposed function, a numerical example is given, the average run length is computed using Markov chain method, and finally, optimal values of parameters are obtained using genetic algorithm. Finally, sensitivity analysis of parameters is performed, and the results indicate that when the slope of covariate function increases, the role of taking multiple measurement decreases, and in the case of measurement error, the optimum values of the parameters are significantly affected.