Using on-line sensors in statistical process control

As manufacturing technology moves toward more computerized automation, statistical process control techniques must adapt to keep pace with the new environment and take advantage of the development in automated on-line sensors. In this paper, a two-phase procedure is proposed for combining an on-line sensor and a control chart to improve statistical process control decisions. In phase 1 of this procedure, a production process is monitored continually by a sensor. When a sensor warning signal is observed, phase 2 takes place: a sample of items is drawn from the process and inspected. If the sample mean is outside the predetermined control limits, the process is stopped, and a search is initiated to determine the actual process status for possible necessary adjustment. If the sample mean is within the control limits, the process continues. A mathematical model is formulated for jointly determining the sample size and the control limit of the control chart and a decision rule for sending out sensor warning signals. The model is based on the assumption that there is only a weak relationship between the sensor measurement and the process condition. A solution algorithm based on a numerical search is developed. A numerical example is used to show the advantage of the proposed model over the models based separately on the sensor and the control chart, and a sensitivity analysis is used to show the effects of several important model parameters on the optimal solution.