The Formula That Validates Your WIP and Lead Time Data

A queueing theorem from 1961 that every lean practitioner should know. If your numbers do not reconcile, your data has a problem.

The formula

L equals lambda times W. L is the average number of items in the system (WIP), lambda is the average arrival rate (throughput), and W is the average time an item spends in the system (lead time). Rearranged: Lead time equals WIP divided by throughput.

Using it as a data quality check

If your WIP is 120 units, your throughput is 30 units per day, and your measured lead time is 5 days, something is wrong. The formula says lead time should be 4 days. Before trusting any VSM analysis, verify that your WIP, throughput, and lead time reconcile through this relationship.

Using it as a design tool

If your throughput is 30 units per day and your target lead time is 3 days, your maximum WIP should be 90 units. More than 90 units in the system and your lead time guarantee is broken by the math. This is how you design supermarkets and kanban quantities: by arithmetic, not by feel.

The leverage

Lead time can be reduced by reducing WIP, increasing throughput, or both. In most operations, reducing WIP is faster and cheaper than increasing throughput. The WIP lever is often available immediately. The throughput lever requires a project.