Question 3 of 7: Metal-Oxide $H_2S$ Sensor — Calibration, Outliers, and Product Liability

Question 3: Metal-Oxide $H_2S$ Sensor — Calibration, Outliers, and Product Liability (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) The best-fit line on the semi-log chart is a straight line, so write $\text{ppm}=10^{\,a-bV}$ for constants $a,b>0$ (concentration falling as output voltage $V$ rises, as stated). Differentiating gives two different, equally valid “sensitivities” depending on which direction is asked for:

The first (ppm change per volt) is LARGEST in magnitude at the HIGH-concentration end (near 100 ppm), because it scales with ppm itself. The second — and the one that actually matters for a safety instrument — is how much the METER's output moves for a given change in the true gas concentration; it is largest, i.e. the sensor is most sensitive by this practical measure, at the LOW-concentration end (near 1 ppm), and it flattens out toward the top of the range. This is the same log-linear behaviour as a Beer–Lambert absorbance curve: because the relationship is exponential, the instrument resolves small CHANGES best exactly where $H_2S$ is most dangerous at low concentration (typical occupational exposure limits sit in the single-digit to low-tens-of-ppm range), and is deliberately coarser once the reading is already deep into the lethal range, where extra resolution adds little practical value.

b) The two outliers should not simply be deleted to make the fit look better — that would be scientific/professional malpractice on a life-safety instrument's calibration record. The correct procedure is to first look for an ASSIGNABLE CAUSE: a momentarily leaking or contaminated calibration-gas line, a reading taken before the sensor's (slower, per part c) response had fully settled, cross- sensitivity to another gas present during that calibration run, or a transcription error. If a specific cause is identified and documented, it is legitimate to exclude those two points from the regression and refit the line, with the reason recorded in the calibration log. If no assignable cause can be found, apply a formal statistical outlier test (e.g. a fixed multiple of the residual standard deviation) rather than excluding points by eye, and retain a record of what was excluded and why — an undocumented, unexplained deletion of inconvenient data is not defensible practice for an instrument whose failure mode is a fatality.

c) A response that is slower coming DOWN (high-to-low) than going UP means that, immediately after a real drop in concentration, the sensor's OUTPUT still lags behind and reads HIGHER than the true (now lower) concentration for some time. To ensure a correct reading after any downward transition, the operator must wait for the LONGER of the two settling times (the slower, high-to-low direction) before trusting the reading, rather than applying the shorter upward settling time uniformly, and should watch for the reading to become stable (no further downward drift) rather than reading at a fixed elapsed time. Where a fast reading is operationally required, the asymmetric lag can instead be characterized and a correction model applied, but the default, always-safe rule is: after a suspected decrease, wait for the slower (high-to-low) response to fully settle.

d) Because $H_2S$ is a fast-acting, lethal gas with a well-documented history of killing agricultural workers, a company selling this sensor faces several distinct liability exposures. First, a duty to warn/instruct: the documentation must clearly and honestly state the instrument's accuracy, its ASYMMETRIC response speed (part c), its minimum detectable concentration, and any known cross-sensitivities — an under-specified device that creates a false sense of safety is a foreseeable contributor to a wrongful-death claim. Second, a duty of care in the calibration and QA/QC process itself — the outlier-handling practice in part (b) is not academic: sloppy or undocumented calibration on a life-safety product is a direct negligence exposure if a miscalibrated unit later fails to warn of a lethal concentration. Third, compliance with the relevant certification standards for gas detectors (e.g. CSA/UL listing, and the applicable occupational exposure limits the device is meant to warn against) is both a regulatory and a liability matter. As a professional engineer, signing off on this product means the design, calibration procedure, and warning labels must all be defensible in the event of an incident — not merely functional under ideal laboratory conditions.