Multi-objective approximation for the optimal design of control charts with variable parameters using the Taguchi loss function

This paper considers an auto-correlated production process represented using a first-order auto-regressive model. During the period when the process is under statistical control, the mean values are contained in their objective value; after the occurrence of an assignable cause, a shift is produced. To detect the occurrence of the assignable cause, we propose a model of control charts with variable parameters to monitor the process and issue warning signals. The technical and economic success of implementing this tool depends on the adequate selection of parameters for the chart such as sample size, sample interval and the coefficient of the control limits. A cost-based model based on the Taguchi loss function was used to select the parameters and multi-objective optimization techniques on the response surfaces to find the optimal levels to minimize the cost and maximize the statistical potential of the chart. The fitting of the multiple regression models was necessary to assess the statistical and economic performance. Subsequently, we constructed a desirability function to simultaneously integrate the statistical and economic design. We identified and quantified the most significant design parameters and the effect of repetition. Finally, we reviewed the impact of the auto-correlation coefficient on the optimal selection of parameters. The results demonstrated that when considering an economic and statistical objective, the sample size is a significant variable in the monitoring of the process.