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 top-half 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.

Drill-down Worksheets

The first three error sources listed in the table can also be evaluated using drill-down 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 built-in 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 Welch-Satterthwaite 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 pre-test 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. In-tolerance 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 pre-test knowledge about the parameter biases, containment limits and associated in-tolerance probabilities can be refined and displayed.