ME.25:5.2 - Change the order of checks without changing the required decision

An administrative procedure accepts a case only if checks A and B both pass. The checks do not change the case or each other’s outcomes. Either may be performed first, and the current requirement permits stopping after the first failure. A takes 6 minutes and passes 90% of cases; B takes 2 minutes and passes 50%. These are supplied proportions for the same incoming population, unaffected by check order. Times are fixed.

With A first, expected effort is 6+0.92=7.8 minutes. With B first it is 2+0.56=5 minutes. Both return the same acceptance decision for every case. The candidate rule is to do B first and run A only after B passes.

For two such checks i and j with fixed costs c_i,c_j and pass probabilities p_i,p_j, placing i first has no greater expected cost when:

c_i + p_i*c_j <= c_j + p_j*c_i,
equivalently c_i*(1-p_j) <= c_j*(1-p_i).

For this two-check comparison, independence of their outcomes is unnecessary: the second check is incurred exactly when the first passes. Extending one fixed ordering rule to many checks needs the conditional probabilities among cases reaching each position; marginal ratios alone can fail when those probabilities change.

Now require the procedure to report every failed condition so that the applicant can correct the case in one return. Stopping after the first failure no longer supplies the required result. Both checks must then be completed, taking 8 minutes of summed effort under the same assumptions. A changed order may still affect the time of an early indication, but it no longer produces the claimed effort saving.

If the requirement instead remains the first-failure decision but A supplies information needed to perform B, the proposed order is unavailable. Add the preparation that would make B independently executable and recompute its cost, or retain A first. A lower algebraic value is not a usable method while its required input is unavailable.

The changed reusable screening rule belongs to method design. Scheduling a particular person’s A check on Tuesday under the unchanged rule would be a Work-planning result.