Solution (source code)

= Solution

Identify the physical coupling that causes a <systematic error> and change the apparatus so that it can be measured or cancelled. <measurement calibration> against known reference standards at several points reveals zero and gain errors; blanks and background runs measure additive contributions. Carry uncertainties of the standards and fitted corrections into the final result.

Reversal provides a particularly transparent test. If $D_+=S+b$ and $D_-=-S+b$, the combination $(D_+-D_-)/2$ isolates $S$ while $(D_++D_-)/2$ measures the <measurement zero offset>. Interleave and repeat the reversals so drift can be detected. The cancellation assumes a stable <measurement zero offset> and a genuinely odd signal; a common gain error remains. <null measurements> and bridge comparisons can reduce dependence on detector gain. Swapping sensors or leads exposes asymmetry; checking alignment, shielding, grounding and <temperature> control tests specific unwanted couplings. Varying signal amplitude or measurement <frequency> can reveal heating, nonlinear response or pickup.

Use independent measurement principles where possible, and test the predicted response to each deliberate change. \b[Repeated readings alone do not remove a fixed <systematic error>.] Correct identified significant effects and retain uncertainty for imperfectly known corrections; complete elimination cannot generally be demonstrated. Type A and Type B classify how uncertainty is evaluated, rather than simply meaning <random measurement errors> and <systematic errors>.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[§§2–5, especially §5.2; Appendix D.1.1.6–D.1.1.8]{ref}