.Credibility.Types.IntervalTolerance

Information

An epistemic uncertainty, i.e. the uncertainty due to lack of knowledge – e.g., on the side of model, analysis or experiment. The uncertainty is described by a nominal value and an interval. See also BaseUncertainty uncertainty for general information.

Often, it is inconvenient to provide absolute ranges of a value and, instead, relative or absolute deviations are more practical. In the eFMI standard (Functional Mock-up Interface for embedded systems), for example, tolerances for reference results are defined in a similar way as tolerances for numerical integration algorithms. Due to its generality, this description form of eFMI is used here as well:

• nominal: nominal value of the scalar. Typically, the nominal value is used as default for the actual parameter value.
• relTol: relative tolerance of limits with respect to nominal (default = 0.0).
• absTol: absolute tolerance of limits with respect to nominal (default = 0.0).

Utilizing this information, the lower and upper values of the underlaid interval distribution can be computed in the following way:

tol = max(absTol, relTol * |nominal|),
lower = nominal − tol,
upper = nominal + tol.

For example, the parameter R of a resistor has the nominal value of 200 Ω, the minimum possible value of 190 Ω and the maximum possible value 210 Ω. Then, the following tolerances can be provided:

• 200 Ω ± 5 % ⇒ parameters unitValue ="Ohm", nominal = 200, relTol = 0.05 (and absTol = 0) or
• (200 ± 10) Ω ⇒ parameters unitValue ="Ohm", nominal = 200, absTol = 10 (and relTol = 0).

Typically, either a description with relTol or with absTol is used, but not a combination of both. On the contrary, there is an important use case where the description with both relTol and absTol is useful: If reference results are provided (e.g. the results of a simulation or an experiment are required to be within some band around a provided reference solution) then a definition with relTol is often practical together with absTol as band for small values of the reference around zero, where relTol makes no sense.