Statistical Methods
Distinguish all scenario combinations from paired inputs
Define the task
Decide whether the design crosses every value of one parameter with every value of another, or pairs values by position. Store a row identifier and column identifier for a crossed design. Draw the expected dimensions before calculating. Multiplication of two equal-length vectors can quietly return only the diagonal.
Carry out the check
Use a deterministic two-argument function to compute one result for each ordered pair. Check units, row labels and column labels. Recompute an off-diagonal cell as well as a diagonal cell. If some combinations are infeasible, keep a reason for their exclusion and avoid interpreting a uniform grid as a probability distribution.
Worked hypothetical example
For hypothetical sample throughput of 2 or 4 specimens per hour and run durations of 3 or 5 hours, the full capacity grid has four values: 6, 10, 12 and 20 specimens. Pairwise multiplication returns just 6 and 20. The crossed grid describes potential capacities under constant rates. Actual workload and downtime need separate inputs.
Method checked 10 November 2026 against R documentation: Outer Product of Arrays.