Instrument Loop Total Error Stackup

WORST CASE AND ROOT SUM SQUARE ANSWER DIFFERENT QUESTIONS AND BOTH ARE LEGITIMATE. The arithmetic sum is what every element erring in the same direction at the same moment would produce -- a real possibility, and the right basis where a single excursion has serious consequences. The root sum square is what independent errors actually combine to most of the time, and it is the right basis for judging whether a loop can do its job. For a typical three-element chain the two differ by roughly 1.3 to 1.7 times, so quoting one and meaning the other over- or understates by a consistent and invisible factor. Both are computed here, with the ratio between them. RSS IS VALID ONLY FOR INDEPENDENT RANDOM ERRORS, which is the caveat most often dropped. A calibration offset, a common ambient temperature effect, or a shared reference error affects several elements in the same direction and must be SUMMED rather than combined in quadrature, and a stackup that quadratures a systematic error is simply understating itself. THE UNIT CONVERSION IS WHERE STACKUPS GO WRONG BEFORE ANY COMBINATION IS ATTEMPTED. Each element quotes its error against its own basis -- degrees, percent of span, percent of reading, counts -- and those bases refer to different quantities, so percentages of different spans do not add. Converting everything to the same engineering units at the measured condition is the work; the combination afterwards is arithmetic. AND THEN THE SENSING ELEMENT'S PLACEMENT MAKES THE WHOLE EXERCISE ACADEMIC. A temperature sensor in a stratified duct, a pressure tap in a turbulent region, a flow element without its straight run, a wall sensor above a heat source -- these produce errors that exceed the entire instrument chain by an order of magnitude, and a carefully computed half-degree stackup sitting under a four-degree stratification is a rounding error. The comparison against the control deadband is what makes it actionable: a loop cannot control tighter than it can measure, and one that cannot will hunt, chase a measurement that depends on which stream its element sits in, and produce a trend that looks like an unstable loop rather than a misplaced sensor. THE REMEDY IS A SENSOR, NOT A TUNING SESSION -- a multi-point averaging element across the duct section, which is a selection rather than a calculation, and the figure it recovers is computed here. This is an uncertainty combination. Published element accuracies are reference accuracies under stated conditions and exclude effects specified separately -- ambient temperature, drift over the calibration interval, supply voltage, mounting position, vibration -- all of which belong in a complete stackup and none of which appear on a headline figure. The installation error is estimated rather than computed and can only be established by measurement, typically by traversing the duct or comparing against a reference at several points. It does not address dynamic error, where a sensor's time constant means it reports a value the process had some time ago, which matters as much as static accuracy in a fast loop. It does not size, select or locate a sensor, specify a calibration interval, or address traceability. The manufacturers' complete specifications including their operating-condition effects, a field verification of the installed measurement, and the controls engineer govern.

each element converted to the same engineering units; worst case = the arithmetic sum; total probable error = sqrt(sum of squares); installation and averaging errors combine in quadrature with the instrument total, and the result is compared with the control deadband.

The worst-case and root-sum-square uncertainty combination conventions. RSS is valid for INDEPENDENT errors only; systematic ones must be summed. Installation error is ENTERED and estimated.

A sum and a root sum square.

Estimate. AHJ and licensed professional govern.

Field names used by the API: span_eng, element_err_eng, transmitter_err_pct_span, input_err_pct_span, installation_err_eng, averaging_err_eng, deadband_eng, element_eng, transmitter_eng, input_eng, worst_case_eng, rss_eng, ratio, element_share_of_worst_pct, total_with_installation_eng, installation_multiple, total_with_averaging_eng

• Errors are independent RSS is wrong for systematic or shared-cause errors, which must be summedstandard uncertainty practice
• Reference accuracies only ambient temperature, drift, supply voltage, mounting and vibration belong in a complete stackupthe manufacturers' full specifications
• Static error only dynamic error from a sensor's time constant is not includeda field verification of the loop