Optimal design of an attribute control chart for monitoring the mean of autocorrelated processes

Several control charts have been proposed to employ attribute inspection to monitor the process mean. However, these control charts are not applicable in many industrial applications where the process variables are highly autocorrelated due to the assumption that the sequence of process observations is statistically independent. Motivated by the simple implementation and good performance of these charts, in this paper, an attribute chart is proposed to monitor the mean of the autocorrelated processes by assuming the distribution of observations follows the First Order Autoregressive (AR(1)) process. To optimally design the proposed chart, a more tractable approach is introduced to compute average run length CARL) by adopting the Stein-Chen method. In addition, a comparison of the proposed control chart with npx chart is presented to investigate the performance of the proposed chart and the effect of autocorrelation. A sensitivity analysis is also provided to study the robustness of the proposed chart. Finally, an industry example is given to illustrate how to apply proposed chart to the manufacturing process.