Condensed from an OPSIS AB article by Bengt Löfstedt, first published 2023-04-20.
Gas concentration measurement is a complex system with many independent sources of uncertainty. A single source may be able to report a value within about one per cent of the true value or better, but once every factor is taken into account the total uncertainty is usually an order of magnitude larger, even when the instrument is performing at its best. Uncertainty is not calculated by imagining the worst possible error from each source and adding them up: the probability of that happening is far too low, since a single error reaching its maximum is already unlikely and all of them doing so in the same direction is much less likely still. The calculation is instead probabilistic, assigning a distribution and a standard deviation to each source and expressing the total usually as a 95% confidence interval. That reduces the weight of any single source and acknowledges that there is no absolutely true uncertainty — only a reasoned estimate of how large it might be. For a type-approved instrument under European rules, the sources and the requirement are set out in EN 15267-3: repeatability, reproducibility, cross-sensitivity, lack of fit, temperature and pressure sensitivity, long-term drift, and the uncertainty of the calibration gas. Each is given a distribution and a standard uncertainty, the combined uncertainty is the square root of the sum of squares, and the expanded uncertainty is twice that, representing the 95th percentile. The result is expressed as a percentage: at the 95% level the reported value must lie within plus or minus a stated percentage of the actual concentration, usually at the emission or air quality limit. The percentage differs by component because some techniques are inherently more uncertain than others: to pass QAL1, total expanded uncertainty must be below 15% for SO2 and NOx, but only below 30% for HCl and HF.
Chinese practice reaches the same idea from a different direction. The HJ 75 series requires a CEMS to be compared with the reference method, and sets limits on the relative error of the comparison, so the uncertainty that matters is the one visible against a manual measurement rather than the one derived from a laboratory budget. That is a practical test, but it has a consequence worth stating: the comparison result depends on sampling, conditioning and timing as much as on the analyser, so a large apparent error does not automatically mean a poor instrument. When a comparison fails, we look at the sample line, the converter, the calibration gas and the timing of the reference sample before touching the analyser. Uncertainty is also the reason not to over-read small differences: two instruments measuring the same duct within a per cent of each other are, in most emission applications, indistinguishable. Report the uncertainty with the number, and the number becomes usable.
Uncertainties in Measurements — read the original at opsis.se ↗
Written by Bengt Löfstedt, OPSIS AB, first published 2023-04-20. The summary and the A.Johnson note above are our own text; the OPSIS article remains the authoritative version. Chinese reader? See the full Chinese article.
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