Perform uncertainty analysis of a measurement
The Measurement Uncertainty Budget in Calibration Control is a simplified budget
where Ape Software assumes no
responsibility or liability for any unintentional errors. It is the User’s responsibility
to ensure
calculations and data entry are accurate and to confirm the suitability for any particular
purpose.
This budget is useful in situations where (a) each Component of
Uncertainty is independent of
the others, (b) the major Components are estimated with a high degree of accuracy,
and
(c) measurement results are measured directly or calculated with a linear
formula using only
multiplication or division (e.g.,
$W=V\times I$
).
Note that each Measurement Uncertainty Budget is conducted for a single Nominal
measurement for a unique piece
of Equipment.
Uncertainty Budget Dialog
 Date: Date the Uncertainty Budget calculations were performed.
 Equipment ID: The unique designation of Equipment a given
study focuses on.
 Nominal: Target value for the overall Uncertainty Budget analysis.

Unit of Measure: Measurement unit (e.g., inches, degrees,
etc.) of the Nominal value
for the Uncertainty Budget analysis.
 Significant Digits: Number places to the right of the decimal.
 Description: Description or title of the Uncertainty Budget
analysis.
 Notes: Any notes relevant to the Uncertainty Budget analysis.
 Standards: Calibration standards/masters used in the study.

Combined [Standard] Uncertainty (${u}_{c}$):
Summation in quadrature (i.e., root sum of the squares) of all the Sources of Uncertainty
in the grid.
$${u}_{c}=\sqrt{\sum _{k=1}^{n}{{u}_{k}}^{2}}$$

Coverage Factor (e.g.,
$k=2$
): Used in the
calculation of the Expanded Uncertainty and has a default value of
$k=2$
.
The Coverage Factor is a confidence level of the interval accounts for the variation in the
estimate of
the residual standard deviation, and is based on the assumption that the random errors have
a normal
distribution.

Expanded Uncertainty ($U$): The Expanded
Uncertainty
($U$) assures a high level of confidence by rescaling the Combined Uncertainty
(${u}_{c}$) expressed with a different confidence
level, e.g., 95
percent. The rescaling is accomplished by multiplying by the coverage factor (i.e.,
$U=k\times {u}_{c}$
). In many
cases, the coverage factor may be 2, which is typically used to approximate a 95% level of confidence.

Expanded Uncertainty Rounded (${U}_{\mathrm{ce}}$):
The expanded uncertainty (${U}_{c}$) rounded
to two significant digits.
Uncertainty Detail Dialog
Use the Detail dialog to describe each source of uncertainty (i.e., Component of
Uncertainty) to be included
in the overall Measurement Uncertainty Budget.

Source Name: Descriptive name for the Source of the Component
of Uncertainty, which
will be combined with other Components to create a single Uncertainty Budget.
 Value ($a$): Numeric value related to
the Unit of Measure.
 Unit of Measure: Units measured in such as inches, Fahrenheit, mph,
etc.

Type A/B: Method used to estimate uncertainty either Type
A, if estimated statistically,
or Type B, if inferred through non statistical methods such as historical measurements, manufacturer
specifications,
calibration certificates, published data, mathematical formulas, or general experience.

[Probability] Distribution: The Probability Distribution
selected dictates the Divisor
(next field). For example, a Normal 1s distribution has a Divisor of 1 where a Normal
2s distribution
has a divisor of 2. The following values for each Probably Distribution are defaulted
into the Divisor
field, which can be overridden.
 No Divisor
 Normal 1s = 1
 Normal 2s = 2
 Normal 3s = 3
 Normal @ 99% = 2.58

 Rectangle =
$\sqrt{3}$
= 1.7321
 Triangle =
$\sqrt{6}$
= 2.4495
 UShaped =
$\sqrt{2}$
= 1.4142
 Rectangle =
$\sqrt{\mathrm{12}}$
= 3.4641


Divisor ($d$): The numeric value related
to the Probability Distribution
chosen. This value is automatically set when choosing the Probability Distribution (previous
field) but
can be edited independently after choosing the Distribution.

Degrees of Freedom ($v$): For Type A
uncertainties, use the d.f. for the
corresponding standard deviations. For Type B sources refer to calibration certificates
or published reports.
In some instances, where the standard deviation must be estimated from scientific judgment
or partial data,
an infinite d.f. is normally assumed.

Sensitivity Coefficient ($c$): Used to
describe how the Component of
Uncertainty contributes to the Combined Uncertainty when a simple functional relationship does
not exist between
the input quantities and the measurement result. For example, the unit of measure for
the study may be in
length units where an Uncertainty Component may be expressed in temperature or angular units.
Use this field
to change the weighting of the Component from the default of 1 (one).

Standard Uncertainty ($u$): Calculated
by dividing the Value
($v$) by the Divisor ($d$) and then multiplying by the
Sensitivity Coefficient
($c$):
$$u=\frac{a}{d}\times c$$

Assumptions Explanation: Use this field to Explain any Assumptions
made for the current
Uncertainty Component.
Learning about Measurement Uncertainty
Here are a few online resources to get started with learning about Measurement Uncertainty.
Here are a few spreadsheet examples of Measurement Uncertainty Budgets:
References
Last updated: 6 Feb 2017
Compatibility: Calibration Control version 8.3 to current