PSD.12:4.3 - Test locally, then expand where the failure can hide

Begin with a cheap discriminating test: a boundary value, an alternative value judgement, an omitted condition, or a direct challenge to one decisive assumption. Recompute the same comparison for all affected alternatives under that changed basis.

Use joint or global variation when interactions, nonlinearities, common causes, thresholds, or structural alternatives can change the result. A one-at-a-time test is insufficient for a claim about those combinations. Use the direct modeling and analysis Method to choose suitable tests, sampling, or proofs; this pattern mandates no universal algorithm or scenario count.

Keep empirical variability, model uncertainty, and value disagreement distinguishable. If a model change alters the meaning or comparability of an output, repair the comparison before treating the difference as another numerical sample.

A computational result is limited by the tested region and procedure. An analytical inequality may establish a whole region under its assumptions; a finite sample usually establishes only sampled behavior unless a further guarantee is justified. State that difference.

PSD.12:4.3.1 - Compare a central response with two equally displaced inputs

Use this small test when the response to a varying input may make a central estimate misleading. It needs a response account suitable for the stated comparison, not an assumed probability distribution.

1. Name the input and the response it affects. Fix the arrangement, affected subject, time window, other relevant conditions, response unit and preferred direction. Choose a central input x and displacement h > 0 so that x-h, x and x+h lie within the account’s admissible domain. Equal input differences and averaging the responses must be meaningful on their respective scales; numerical labels alone do not suffice.
2. Obtain the three comparable response values from the qualified model or suitable observations. For response r, calculate the endpoint mean and its difference from the central response: D = (r(x-h) + r(x+h))/2 - r(x). The equal weights define this constructed test. Calling the mean a real-world expectation requires a separately qualified probability model.
3. Interpret D on the declared response coordinate. A positive difference means the endpoint mean exceeds the central response: worse for a loss, better for a benefit whose higher value is preferred. For a target-valued response, use its declared preference rule. Zero means no midpoint gap at these three points; it does not prove linearity or robustness over an interval. Examine each tested response against any independently justified threshold as well.
4. Widen the displacement or test another consequential condition only when it could change the receiving decision and the model’s domain permits it. Report the tested values and gaps; do not turn one finite comparison into a regional convexity, derivative or global robustness claim.

If the response account or scale is inadequate, return that specific limit. A clearly conditional calculation or qualitative comparison may remain useful; requesting more observations is a separate worth question, not an automatic next step.

When a harmful response suggests changing exposure, formulate the actual alternative arrangement and compare its whole contribution through C.11.CRC. Include the means, carrying burden and displaced work required to maintain a proposed protection. A stated spending limit alone does not enforce a consequence limit. C.16 governs quantity and scale use; C.29 governs a needed mathematical-representation correspondence and its transfer limits. The robustness account remains the result here.