Run length distributions for estimated attributes charts

Attributes control charts, such as c and p charts, are popular methods for detecting out of control signals when it is practical only to obtain qualitative information about a process; in such cases, variables control charts, such as the , s and R charts, cannot be used. The run length distributions have previously been studied for variables charts when the control limits have been estimated. Little has been done in the case of attributes charts. In this paper, the run length distributions for the c chart and p chart are derived for the case when the control limits are estimated. It is shown that, as for variables charts, the effect of estimation on quantities such as the average run length (ARL) can be quite dramatic, but when the underlying process is in control, the ARL is potentially misleading as a basis for comparison. Received: September 1998