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rtd_sensor.uncertainty

The core uncertainty helpers, resistance propagation, and temperature-budget APIs were introduced in project release 0.3.0 under pt100-core / rtd; their current rtd_sensor.uncertainty import path began with rtd-sensor 0.4.0. Fitted-parameter covariance propagation into resistance and inferred temperature was added in rtd-sensor 0.7.0.

Type aliases

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

BoundDistribution = Literal["rectangular", "triangular"]
EvaluationMethod = Literal["A", "B"]

RTDUncertaintyModel

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

A structural protocol requiring resistance-to-temperature conversion and local dT/dR sensitivity. Full RTDModel objects satisfy this narrower uncertainty interface.

Scalar helpers

All four scalar helpers were introduced in project release 0.3.0; current rtd_sensor.uncertainty paths date to rtd-sensor 0.4.0.

standard_uncertainty_from_bound(
    half_width: float,
    *,
    distribution: BoundDistribution,
) -> float

standard_uncertainty_from_expanded(
    expanded_uncertainty_value: float,
    *,
    coverage_factor: float,
) -> float

combine_independent_standard_uncertainties(
    *standard_uncertainties: float,
) -> float

expanded_uncertainty(
    combined_standard_uncertainty: float,
    *,
    coverage_factor: float,
) -> float

TemperatureUncertaintyComponent

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

TemperatureUncertaintyComponent(
    name: str,
    standard_uncertainty_c: float,
    evaluation_method: Literal["A", "B"] | None = None,
    source: str | None = None,
    note: str | None = None,
)

ResistanceUncertaintyPropagation

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

Result fields:

resistance_ohms: float
temperature_c: float
resistance_standard_uncertainty_ohms: float
temperature_sensitivity_celsius_per_ohm: float
temperature_standard_uncertainty_c: float

propagate_resistance_uncertainty

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

propagate_resistance_uncertainty(
    resistance_ohms: float,
    resistance_standard_uncertainty_ohms: float,
    *,
    model: RTDUncertaintyModel,
) -> ResistanceUncertaintyPropagation

TemperatureUncertaintyBudget

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

Result fields:

resistance: ResistanceUncertaintyPropagation
additional_components: tuple[TemperatureUncertaintyComponent, ...]
combined_standard_uncertainty_c: float
coverage_factor: float | None
expanded_uncertainty_c: float | None
temperature_c: float  # read-only property

temperature_uncertainty_budget

Introduced in: project release 0.3.0 (pt100-core); current import path since rtd-sensor 0.4.0.

temperature_uncertainty_budget(
    resistance_ohms: float,
    resistance_standard_uncertainty_ohms: float,
    *,
    model: RTDUncertaintyModel,
    additional_components: Iterable[TemperatureUncertaintyComponent] = (),
    coverage_factor: float | None = None,
) -> TemperatureUncertaintyBudget

FitCovarianceResistancePropagation

Introduced in: rtd-sensor 0.7.0.

Result fields:

temperature_c: float
resistance_ohms: float
parameter_covariance: FitParameterCovariance
parameter_sensitivity_vector: tuple[float, ...]
resistance_variance_ohms_squared: float
resistance_standard_uncertainty_ohms: float

The sensitivity vector follows the covariance parameter order and represents dR/dtheta for the fitted parameters. Individual sensitivity entries may have different physical dimensions because the parameters themselves can have different dimensions.

propagate_fit_covariance_to_resistance

Introduced in: rtd-sensor 0.7.0.

propagate_fit_covariance_to_resistance(
    temperature_c: float,
    *,
    fit_result: CallendarVanDusenFitResult | IEC60751R0FitResult | PolynomialFitResult,
) -> FitCovarianceResistancePropagation

Applies covariance propagation J Cov(theta) J.T to the parameter covariance retained by a supported fit. For IEC-R0 and polynomial fit-space parameterizations, resistance is linear in the retained parameters, so the resistance covariance transformation is exact at fixed temperature. For custom CVD fits, covariance is retained in the public R0/A/B/C parameter basis; when R0 and shape coefficients are jointly estimated, forward propagation is a first-order local transformation because those parameters enter multiplicatively. The fit must have available parameter covariance. This result covers fitted-model uncertainty only; it does not automatically combine acquisition uncertainty, reference-temperature uncertainty, drift, tolerance, or other budget components.

See Measurement & uncertainty.

FitCovarianceTemperaturePropagation

Introduced in: rtd-sensor 0.7.0.

Result fields:

resistance_ohms: float
temperature_c: float
parameter_covariance: FitParameterCovariance
resistance_parameter_sensitivity_vector: tuple[float, ...]
temperature_sensitivity_celsius_per_ohm: float
parameter_sensitivity_vector: tuple[float, ...]
temperature_variance_celsius_squared: float
temperature_standard_uncertainty_c: float

parameter_sensitivity_vector follows the covariance parameter order and represents dT/dtheta for the fitted parameters with the measured resistance held fixed. It is obtained from the retained resistance-parameter sensitivities and the model's local inverse sensitivity.

propagate_fit_covariance_to_temperature

Introduced in: rtd-sensor 0.7.0.

propagate_fit_covariance_to_temperature(
    resistance_ohms: float,
    *,
    fit_result: CallendarVanDusenFitResult | IEC60751R0FitResult | PolynomialFitResult,
) -> FitCovarianceTemperaturePropagation

Converts the supplied resistance with the fitted model and propagates the full retained parameter covariance into inferred temperature using the implicit first-order sensitivity

dT/dtheta = -(dR/dtheta) * (dT/dR)

The resistance is treated as fixed. This result therefore covers fitted-model parameter uncertainty only; uncertainty in the resistance measurement itself, reference-temperature uncertainty, drift, tolerance, and other budget components remain separate.

See Fitted-model covariance propagation.