A wire's diameter is measured with a micrometer

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 wire's diameter is measured with a micrometer. Four contributions to the uncertainty budget have been evaluated: the scatter of five repeated closures on the wire,

u = 0.0021\,\mathrm{mm}

, evaluated from the standard deviation of the readings (Type A); the zero-point (jaw-closure) correction, estimated from twenty repeated closures on the jaws alone with nothing between them,

u = 0.0015\,\mathrm{mm}

, again from the scatter of repeated readings (Type A); the manufacturer's specification, a bound of

\pm0.005\,\mathrm{mm}

on any single reading, treated as rectangular (Type B), giving

u = 0.005/\sqrt3 = 0.0029\,\mathrm{mm}

; a bound of

\pm0.001\,\mathrm{mm}

on thermal expansion of the wire between calibration and measurement, treated as rectangular (Type B), giving

u = 0.001/\sqrt3 = 0.00058\,\mathrm{mm}

. All four sensitivity coefficients are

1

. A laboratory report combines them as follows: 'Type A means a random effect and Type B means a systematic one, so they cannot be mixed. The Type A total is

u_{\rm A} = \sqrt{0.0021^2 + 0.0015^2} = 0.0026\,\mathrm{mm}

and the Type B total is

u_{\rm B} = \sqrt{0.0029^2 + 0.00058^2} = 0.0030\,\mathrm{mm}

. The combined standard uncertainty is their sum,

u_{\rm c} = u_{\rm A} + u_{\rm B} = 0.0056\,\mathrm{mm}

.' ((a)) State the error in this reasoning. ((b)) Give the correct combined standard uncertainty

u_{\rm c}

, to two significant figures.

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