On a direct estimator for average production intervals

Nozari and Whitt proposed an indirect approach to estimating the average production interval (i.e., the length of time between starting and finishing work on each good or defect-free product), based on measurements of the work-in-process inventory and the production rate. A necessary and sufficient conditon for the consistency or validity of their estimator is derived herein. The present validity condition also yields an alternate estimator for the average production interval; as a direct estimator, it has better asymptotic efficiency than the indirect estimator.