Estimating the rate at which a process goes out of control in a statistical process control context

Models for the economic design of control charts have, in the past, implici tly assumed that the rate at which the process goes out of control is known or can be easily estimated. It is suggested that there are difficulties wi th this assumption; in particular, the most obvious estimators generally pe rform badly. Four estimators for this rate are developed and simulation exp erimental results are presented on the performance of each. A maximum likel ihood estimator and an estimator that incorporates an exact expression for the expected time until the process goes out of control provide the best pe rformance in general. However, there are some situations in which a naive e stimator can perform best. Interpretation of the results provides insights for estimating the unknown rate in practice.