C.43:5.1 - A measurement is useful only through an available response

A workshop can run a batch quickly or cautiously. For a constructed comparison, suppose an agreed net outcome score is 100 for fast operation in a good material state, −20 for fast operation in a bad state, and 40 for cautious operation in either. The two material states initially have equal probability. These are illustrative decision values after the included operating costs, not observed production data or interpersonal utility measurements.

Without another observation, either action has expected score 40. A test costing 5 has accuracy 0.8 in each state and does not change the material or delay the decision. A good test result gives probability 0.8 of good material: fast operation then has expected score 76. After a bad test result, its expected score is 4, so cautious operation is preferable at 40. Each result has probability one half. The conditional continuation obtains 0.5 × 76 + 0.5 × 40 − 5 = 53, a gain of 13.

The construction uses more than the test’s accuracy. It uses the conditional future choice. If the future action is fixed before the test, either fixed action gives 40 − 5 = 35. If testing instead consumes the only fast-operation window, the available post-test action is cautious and again gives 35. The same informational accuracy then has a different practical value because the continuation changed.

Now suppose outsourcing the batch is feasible, gives 55 under the same basis, and remains available after the test. Without testing, outsourcing is the best available continuation. With testing, choose fast operation after a good result and outsource after a bad one: 0.5 × 76 + 0.5 × 55 − 5 = 60.5. The net informational gain is now 5.5 relative to the best available continuation, not 20.5 relative to current cautious operation. Adding a feasible alternative changes both the conditional policy and the value of testing. If the outsourcing offer instead expires before the test returns, that combined policy is unavailable; compare its immediate 55 with the original test-based 53.

During use, the operator checks the assumption that test delay leaves both actions available and that the observed test characteristics apply to this material. If either premise changes, revise the dependent comparison. The result does not require redesigning the workshop’s control architecture.