On Optimal Setting of Control Limits for Geometric Chart

Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment.