C.16.IR:5.2 - A saturated reading can settle one threshold

An ideal instrument reports r = min(y,10), where y ≥ 0 is a quantity expressed on the instrument’s stated scale. For r = 10, every y ≥ 10 is compatible.

If the working question is y ≥ 8, the reading settles it. If the question is y ≥ 12, y = 10 and y = 13 are compatible cases with different answers. Reporting y = 10 as the determined quantity would lose that distinction.

Now suppose the reported reading follows r = min(y,10) + e, with -0.2 ≤ e ≤ 0.2. This error is applied after the clipping operation. For the same r = 10, the ideal clipped value can lie from 9.8 to 10. The compatible set becomes y ≥ 9.8: y = 9.8 with e = 0.2 is a feasible endpoint, and every y ≥ 10 fits with e = 0.

The reading still settles y ≥ 8. It no longer settles y ≥ 10, since y = 9.8 and y = 10 are both compatible. This is a bound-based result; no probability was assigned to the error. Repeated readings do not narrow that bound merely by being repeated. A narrower result needs a relation that supports the reduction, such as a justified stochastic error model or a smaller error bound.