Combined adaptive sample size and sampling interval X̄ control scheme

A conventional X̄ control chart works in an open loop manner. That is, the process control engineer waits until the control scheme signals an out-of-control condition. This paper proposes a combined adaptive X̄ chart that uses real-time, dynamic information available from the process to make the control scheme pro-active. The procedure consists of a simple method of varying the control chart design parameters (sample size and sampling interval) between minimum and maximum values depending on the current state of the process. The proposed procedure is compared with the standard Shewhart X̄ chart, a variable sample size chart, and a variable sampling interval chart in terms of the average time to signal an off-target process. Substantial improvement in the performance over these schemes is demonstrated. Optimal values for the maximum sample size are also given. The advantages of using the combined adaptive chart is illustrated by an example from a production process.