Control charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS) X¯ control chart is considered for the economic design using nonlinear mixed integer programming approach. The triple sampling (TS) X¯ control charts are developed for economic design based on the results of solving the DS X¯ chart design problems. In this model, we assume that the process must be shut down during the search for the assignable cause. Multiple sampling X¯ charts can be designed for quick detection of a small shift in process. The results of the comparison between the economic-statistical design of DS and TS X¯ control charts show that TS X¯ control charts are more efficient in terms of minimizing the average sample size, but its expected average cost takes larger values.

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