OPS.10.1:4.5 - Obtain the needed probability or protective bound

For a finite probability question, specify the joint uncertain inputs, initial state and operating policy. When a policy adapts during execution, base each choice on information available at that time. Separate schedules chosen after each complete outcome is known do not establish one policy that can be executed. When there are few combinations of uncertain inputs, enumerate them; otherwise generate paths from that joint model and apply the event rules to each path. For each path, test the stated service predicate, such as both named orders complete by hour four. Aggregate by the paths’ probabilities, or estimate the probability with the sampling uncertainty needed by the decision. MMP.7/.13 and CMP.9 supply observation, inference and sampling methods when those contributions are needed.

Preserve dependence between arrivals, service durations, outages and returns. Equal marginal means or distributions do not make different joint models equivalent. Section 5.2 changes only service dependence and changes the probability while preserving the mean completion time.

A scenario without probabilities supports a conditional consequence. A family of bounded disturbances can support a protective bound if the response is shown to work for every disturbance in that family. One successful replay supplies only its case. A mean replenishment time multiplied by a consumption rate gives no such worst-case or probability statement by itself.

Include the starting backlog and horizon for a transient service question. Use a continuing-regime mean only for the mean question it answers. For an empirical claim, interpret source coverage and input/model uncertainty as well as calculation or sampling error. Obtain another observation only if the unresolved difference can alter the receiving decision.