Estimating Average Production Intervals Using Inventory Measurements: Little's Law for Partially Observable Processes

Abstract

This paper proposes an indirect approach to estimate average production intervals (the length of time between starting and finishing work on each product) using work-in-process inventory measurements. The idea is to apply a modified version of Little's law (L = λW) from queueing theory to cope with stochastic processes that are not directly observable. When the actual amount of completed product to be produced from the current work-in-process is not known, we suggest working with an appropriate expected amount of completed product associated with current work-in-process, taking care to properly account for such features as partial yields, changing lot sizes and reconstituted lots. This indirect estimation procedure can be applied to computer simulation as well as direct system measurement. The approach also can be used to calculate expected values of steady-state random variables in mathematical models.