Marginal service rates do not identify the joint perfect-order rate
A fictional supplier report states that ninety percent of orders were on time and ninety percent were complete. It does not say which specific orders met each condition or whether the events are independent. A colleague multiplies the percentages and reports eighty-one percent as the observed on-time-in-full result. Another asks for the joint order-level definition and relevant records. This written exercise evaluates no real supplier and sends no report. It asks the learner to distinguish marginal percentages from a joint event, explain what additional assumption a multiplication model would need and identify the kind of evidence required to report the actual customer-service measure accurately.
1. Why is 81%not established as the observed joint rate?
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The two marginals do not show their overlap. Multiplication requires an appropriate independence or conditional-rate model, not merely two percentages.
2. What evidence supports the actual joint metric?
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Use the defined eligible order population and identify orders satisfying both conditions, with consistent commitments and data. State a hypothetical multiplication assumption explicitly if only modeling is intended.