OPS.11.1:4.4 - Connect the quantities and events across scales

Choose the relationship needed between the accounts. Sometimes a wider quantity is a sum of disjoint local quantities. Sometimes it is a union, a maximum, a rate over an interval or a conditional response. Derive that operation from the receiving question.

For example, an order requiring every component becomes ready at the latest required component completion, provided no further work remains. Adding component completion times would describe neither that event nor the elapsed time. Parts processed together in a feasible machine batch share its occupation; take the union of that machine’s occupied intervals when calculating its busy time.

When aggregating, preserve the condition under which the summary is usable. A department’s average service rate may help a sustained-load question but leave the deadline of a particular batch unresolved. A sample-count summary may omit which order is waiting for its final sample.

To construct a sufficient summary, first express the requested result in the quantities you propose to retain. Derive the answer from those quantities and their stated conditions. If an omitted detail still enters the answer, look for two allowed arrangements with the same summary and different answers. Such a pair disproves sufficiency; failing to find one does not establish it. Retain the distinguishing relation, derive a useful bound, or restrict the answer. In the laboratory case below, the sample-to-order relation and the latest required completion provide the order’s completion event; sample totals alone cannot. C.29.1 develops this construction and preservation question. MMP.18 constructs compatible exchanges when mathematical models must be coupled, including shared quantities, time scales, feedback and uncertainty.