Diagnose queues and effective capacity

In an engineering review service, every engineer can be busy all day while the number of waiting packages grows. Utilization describes how people's time is used; flow counts packages crossing a defined boundary in a period. Define the system first. Does it start when a complete package arrives or when the client requests work? Does it end at the first comment or final approval? Do not compare requests entering early design with approvals leaving a later gate as if no rework or pauses existed between them. Map four states: ready for review, being reviewed, returned for correction, and accepted. If a returned package is logged as a new package, measured productivity can change even though the actual service has not.

Suppose six complete packages arrive each week and the team finishes five approvals each week for four weeks. With an unchanged package definition and no withdrawals, unfinished inventory grows by one package per week, adding four to its opening balance. Renaming waiting as 'active work' does not close that gap. Ask where packages spend time: before first review, between disciplines, or in redesign? Adding first reviewers may not increase output if approval by a second discipline is the constraint. Holding back incomplete packages may reduce the visible queue but does not demonstrate a higher approval capacity. Measure queue size and accepted output separately.

Little's law relates average work in progress to throughput and average time in a stable, consistently bounded system: work in progress equals throughput times cycle time. If average work in progress is 18 packages and a stable system completes 6 each week, average time in system is 18÷6=3 weeks. That is not a promise that each package takes exactly three weeks; variation may be large. If eight arrive weekly but only six leave, inventory is growing and 18÷6 must not be presented as a stable future cycle time. Check the period, entry and exit definitions, and inventory stability before using the relation. Even in a stable system, a decision maker also needs package-age distribution and the proportion of priority packages missing target dates, not only the mean.

Rework may seem like pure waste, yet some returns catch a defect before construction. Do not recommend abolishing them to improve an output indicator. Separate returns caused by missing inputs at submission from those caused by a defect found by a sound review; they call for different remedies. The share of complete inputs is worth tracking, but define 'complete' by a fixed checklist or the number can improve simply by weakening the label. In the advisory memo, state what inventory reconciliation establishes, what it cannot establish about the constraint or output safety, and a short, proportionate evidence-gathering step. Team capacity is not its average busyness; it is the rate at which the whole system produces accepted outcomes within quality and safety constraints.