OPS.15.1:5 - Archetypal Grounding

OPS.15.1:5.1 - A window cuts through unfinished work

Observe an operation from hour zero to hour eight. Case A arrived at minus three and leaves at two. B arrives at one and leaves at four. C arrives at six and is still present at eight.

The population-time area is seven case-hours, so mean population is 7/8. Counting departures gives two in eight hours. Their full residence mean is four hours; multiplying 2/8 by four gives one, not 7/8.

There is no contradiction. The departure cohort includes three hours of A before the observation window and excludes C’s two observed hours. Computing the clipped intervals answers the window question. C’s eventual completion is unnecessary for that result.

Now the question changes to the mean full residence of all three cases. C’s endpoint matters. If no later information is available, the sum is at least ten hours and the mean at least 10/3, with no supported finite upper bound. The earlier mean population does not fill that missing endpoint.

OPS.15.1:5.2 - One batch, several parts, one machine

A machine processes three parts together from minute zero to thirty. The completion event is linked to all three parts. The machine is otherwise available throughout a sixty-minute observation window.

The batch occupies thirty machine-minutes: utilization under this occupied-time definition is 30/60. The parts accumulate ninety part-minutes of batch residence. Copying the cycle interval into three part records preserves each part’s history but does not create ninety machine-minutes.

Part 2 requires another ten-minute cycle from minute forty to fifty. Machine occupation becomes forty minutes and utilization 40/60. There are three distinct parts and four processing visits. The returned part’s additional visit consumes capacity while its customer-level completion follows the acceptance rule.

If an operator attends only loading and unloading, machine occupation does not establish operator attention time. Recover those intervals before making a staffing claim.

OPS.15.1:5.3 - An unknown endpoint need not stop the decision

One uninterrupted processing episode starts at hour ten. A reliable observation shows it still in progress at fourteen and a later observation shows completion by twenty. The elapsed processing duration is bounded by four and ten hours; its precise endpoint is unknown.

A question about completion by eighteen remains unresolved. A question about completion by twenty-two is already settled by the observation at twenty. The second decision needs no search for the precise endpoint. If the claim instead concerns uninterrupted duration and interruption was possible but unobserved, that premise must be revisited before using the duration bound.

These cases are constructed demonstrations of the measurement operations.