A stable queue and a WIP experiment
A fictional delivery service has a stable long-run average of twelve items within its defined work boundary and completes four items per week. That boundary begins when the team accepts an item and ends when it is delivered to the customer. The team suspects that excessive simultaneous work contributes to waiting, but it has not yet tested the effect of a new work-in-progress limit. A manager proposes announcing that halving the posted limit will certainly halve delivery time even if staffing, item size, dependencies and throughput all change. The experiment will run with a clear review date and measure actual average WIP, throughput, lead time and quality. The supplied initial averages satisfy the conditions needed for the simple Little’s Law calculation, without claiming that every transient week is stable.
1. Calculate initial average lead time and state the condition for a halving prediction.
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Initial average lead time is 12/4 =3 weeks. If the same stable boundary later has average WIP 6 and unchanged throughput 4 per week, the corresponding average is 1.5 weeks. Lowering a posted limit alone does not prove either new average.
2. Choose evidence for the review.
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Measure actual WIP, completed throughput, elapsed times and quality over a useful comparable period. Inspect blocked work, dependencies and item-size changes. Retain or revise the intervention based on evidence instead of treating the limit as guaranteed performance.