Measurement Process Uncertainty Worksheet Features
Measurement process errors may arise from several sources
including measurement system bias, measurement procedures, measuring environments, measurement system operation, the perception and interpretation of measurement results and from a variety of other sources.
The uncertainty due to these errors is analyzed using the Measurement Process Uncertainty
Worksheet, which is activated by selecting Uncertainty on the Main
Screen menu or by clicking the corresponding icon on the Toolbar.
This worksheet was developed for conducting rudimentary uncertainty analyses using a subset of the capabilities of
ISG's UncertaintyAnalyzer
program. AccuracyRatio is also designed to import data and results
directly from UncertaintyAnalyzer. Brief descriptions of the worksheet features and
functions are given below.
Menu
Bar
Worksheet
entries are accepted and the worksheet closed by selecting OK on
the menu. Conversely, new entries or changes are ignored and the
worksheet closed by selecting Cancel. Worksheet
entries can be cut, copied, pasted, or deleted via the Edit menu. Selecting
Run opens the Run
External Application Screen, which can be used to launch external
Windows applications from within AccuracyRatio. Selecting Enter
Data gives you options for entering measurement data for the measuring
parameter and/or subject parameter. Selecting Correlations
opens the Correlation
Coefficients List Screen, which is used to establish correlations
between error sources. UncertaintyAnalyzer data and analysis
results can be imported into the worksheet via the Import
menu. A process error distribution plot can be displayed by
selecting Plot.
Tool Bar
The Tool bar provides icons that can be used to access selected
options and functions. A brief description of the associated
function or options can be obtained by placing the mouse cursor over the
icon of interest.
Measurement
Process Errors
Table
The tophalf of the worksheet contains a table showing the error sources
that can be accommodated by AccuracyRatio. The Error Source column contains a list of measurement process error sources,
which include: MTE Bias, MTE Random, SU Random, MTE
Resolution, SU Resolution, Data Acquisition, Stress Response,
Environment, and User Defined. The
description labels for all error sources except MTE Bias, MTE Random and SU Random
can be modified, if desired, by clicking the label and typing a new
name. These revised descriptions will be reflected in printed reports and on the Correlation Coefficients
List Screen. If uncertainties are imported from UncertaintyAnalyzer, the appropriate labels will be imported also.
The Error Limits
column shows limits that are expected to contain process errors with some level of confidence. Error limits are also referred to as confidence limits or containment limits.
Error limits and associated confidence level (% Confidence) can be input directly. In this case, the standard uncertainty
(Uncertainty) is
computed based on these values and the associated degrees of freedom (Deg
Fdm) are
considered to infinite. Alternatively, error limits can be
computed from entered values for the standard uncertainty, degrees of
freedom and confidence level. Error limits and standard
uncertainty values are entered/displayed in
subject parameter tolerance units.
The
% Confidence column lists the confidence level or probability that a process error will fall within its displayed error limits.
For this reason, the confidence level is sometimes called the
containment probability. The
% Confidence for each process error is typically entered directly, but
will be computed if error limits and standard uncertainty values are
entered.
The
Deg Fdm column lists the degrees of freedom for the uncertainty in the corresponding
error source.
The degrees of freedom quantify the amount of information on which an uncertainty estimate is based. For samples of measurement results, the degrees of freedom is the sample size minus one.
If
a random uncertainty is computed from a sample entered in the Data Entry
Screen (see below), the degrees of freedom are displayed automatically.
For estimates obtained heuristically, the degrees of freedom must
be entered manually (unless imported from UncertaintyAnalyzer).
If left blank, the degrees of freedom are taken to be infinite.
The
Uncertainty column displays the estimated standard uncertainty for the selected error source.
This value may be entered or computed from entered error limits, confidence level and
degrees of freedom. The Include column allows you to select which error sources to include in computing the
total process uncertainty estimate.
Drilldown
Worksheets
The
first three error sources listed in the table can also be evaluated
using drilldown analysis worksheets. The measuring parameter bias
uncertainty can be estimated using the
Parameter Bias Uncertainty
Worksheet, which is accessed by clicking the
MTE Bias button. The random uncertainty in measurements made using
the measuring parameter and/or subject parameter can be calculated statistically by entering measurement results
in the builtin Data Entry
Worksheets, which are accessed by clicking the MTE Random and
SU Random buttons.
Total
Process Uncertainty
This section of the worksheet displays the total process uncertainty,
its units, and
associated degrees of freedom. The total process uncertainty,
excluding MTE bias, is also displayed along with the associated degrees
of freedom. The Include in Analysis check box provides the
option of including the uncertainty analysis results in risk assessment.
Whenever information is updated in an Error Limits, % Confidence, Deg Fdm or Uncertainty box, if the associated Include box is checked, AccuracyRatio
automatically recalculates the total process uncertainty. The
calculation of the total process uncertainty also incorporates any
correlation coefficients that have been established between process
error sources via the Correlation Coefficients List Screen. The
associated degrees of freedom are computed using the WelchSatterthwaite
formula.
Parameter Bias Uncertainty Analysis
This
section of the worksheet displays the results of an analysis method called SMPC (Statistical Measurement Process Control). SMPC utilizes pretest knowledge, measurement data and uncertainty analysis results to develop what are called "Bayesian" estimates of both subject parameter bias, measuring parameter bias and associated
bias uncertainties. Intolerance probabilities at the time of
measurement are also estimated for both parameters.
SMPC analysis results can be displayed if both the subject parameter and
measuring parameter biases are estimated (via the Parameter Bias
Uncertainty Worksheet). These estimates comprise what is known about the "accuracies" of the subject and measuring parameters
at the time of measurement.
SMPC analysis also requires that a
sample of measurements be taken by the subject parameter and/or
measuring parameter and entered in the Parameter Data Entry Worksheet(s).
With this additional measurement information, the pretest
knowledge about the parameter biases, containment limits and
associated intolerance probabilities can be refined and
displayed.
