Averaging and Acceptance Gates

Averaging Rejects a Drifting Run

A drifting run can pass through the same average formula but fail the residual-budget gate that checks whether readings still cluster around the target. The rejection is exact for the stated readings and limit; real drift estimates depend on calibration history, time ordering, correlated noise, outlier policy, and model choice.

A finite squared-residual budget can reject a drifting run. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A drifting run can average away from the target

Readings 8, 10, 12, 14 volts average to 11 volts.

Vˉ=11 V\bar V=11\ \text{V}
Drifting runThe target and average are separate checked labels.readings=8,10,12,14 Vtarget=10 Vaverage=11 Vresiduals=-2,0,2,4squaredBudget=24gateLimit=4acceptedBit=0 bit

The squared residual budget rejects the run

Residuals -2, 0, 2, 4 give budget 24, which is above limit 4, so accepted bit is 0.

4+0+4+16=24>44+0+4+16=24>4
Rejected finite gateThis is a finite gate, not stochastic confidence.readings=8,10,12,14 Vtarget=10 Vaverage=11 Vresiduals=-2,0,2,4squaredBudget=24gateLimit=4acceptedBit=0 bit