A steel sphere's diameter has four rows in its uncertainty budget: Type A

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Type A, Type B and the uncertainty budget

Problem

A steel sphere's diameter

d

has four rows in its uncertainty budget: Type A, repeated micrometer readings (

N=8

s=0.06\,\mathrm{mm}

u = 0.0212\,\mathrm{mm}

. Type A, comparison against a reference sphere over

20

paired measurements (a correction with best estimate zero):

u = 0.010\,\mathrm{mm}

. Type B, the micrometer's

0.01\,\mathrm{mm}

display resolution:

u = 0.00289\,\mathrm{mm}

. Type B, the micrometer's calibration certificate,

\pm0.03\,\mathrm{mm}

k=2

u = 0.015\,\mathrm{mm}

. Someone argues: "Two of these rows are Type A (random error) and two are Type B (systematic error), so they cannot be mixed. First combine within each type:

u_{\rm A}=\sqrt{0.0212^2+0.010^2}=0.0236\,\mathrm{mm}

and

u_{\rm B}=\sqrt{0.00289^2+0.015^2}=0.0153\,\mathrm{mm}

. The total uncertainty is then the sum of the two totals,

u_{\rm A}+u_{\rm B}=0.0389\,\mathrm{mm}

, since random and systematic effects are different kinds of thing." ((a)) Identify the error or errors in this reasoning. ((b)) Compute the correct combined standard uncertainty

u_{\rm c}(d)

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