A digital length indicator (a comparator gauge) is calibrated against two certified…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Uncertainty in measurement

Measurement and Method, Ch The instrument: resolution, sensitivity, calibration and traceability

Problem

A digital length indicator (a comparator gauge) is calibrated against two certified gauge blocks, whose lengths are known to far better precision than the indicator and are treated as exact. Against a

5.000\,\mathrm{mm}

block the indicator reads

I_1 = 5.008\,\mathrm{mm}

. Against a

20.000\,\mathrm{mm}

block the indicator reads

I_2 = 20.031\,\mathrm{mm}

. By repeating a reading several times, the indicator's repeatability is found to be

\pm0.002\,\mathrm{mm}

, and this applies to every reading it gives, including the two calibration readings above. The indicator is then used to measure a component and displays

12.500\,\mathrm{mm}

. ((a)) Fit the straight line True

=a+b\times

Indicated through the two calibration points, and use it to find the corrected length corresponding to the displayed

12.500\,\mathrm{mm}

. ((b)) Suppose both calibration readings had happened to be biased together, in the same direction, by the full

\pm0.002\,\mathrm{mm}

repeatability (the worst case, since raising either one lowers the corrected length), and recompute the correction to see how much it would shift. Add the component reading's own

\pm0.002\,\mathrm{mm}

repeatability directly to this shift (no quadrature) to obtain a bound on the corrected length.

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