.Credibility.Types.TruncatedNormalTolerance

Information

A truncated normally distributed uncertainty. The minimum and the maximum possible value of the uncertain scalar is described by a nominal value and an interval. See also BaseUncertainty uncertainty for general information.

Similarly to IntervalTolerance, this description utilizes:

• 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).

And, additionally,

• stdDevFactor: factor of tolerance to standard deviation of (non-truncated) normal distribution.

Consequently, the parameters of the underlaid truncated normal distribution, are computed from the given parameterization in the following way:

tol = max(absTol, relTol * |nominal|)
lower = nominal − tol
upper = nominal + tol
stdDev = tol/stdDevFactor

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. These limits are considered being at 2*stdDev (standard deviation σ) of the non-truncated normal distribution, i.e. at a probability of 95.4 %. This yields the following parameters of truncated normal distribution:

• 200 Ω ± 5 %, 2σ ⇒ parameters unitValue ="Ohm", nominal = 200, relTol = 0.05 (and absTol = 0), stdDevFactor = 2 or
• (200 ± 10) Ω, 2σ ⇒ parameters unitValue ="Ohm", nominal = 200, absTol = 10 (and relTol = 0), stdDevFactor = 2.