Overview of Measurement Systems Analysis

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The EMP (Evaluating the Measurement Process) method in the Measurement Systems Analysis platform is largely based on the methods presented in Donald J. Wheeler’s book EMP III Using Imperfect Data (2006). The EMP method provides visual information and results that are easy to interpret and helps you improve your measurement system to its full potential.

The Gauge R&R method analyzes how much of the variability is due to operator variation (reproducibility) and measurement variation (repeatability). Gauge R&R is available for many combinations of crossed and nested models, regardless of whether the model is balanced. For more information, see the “Variability Gauge Charts” chapter.

Within the Six Sigma DMAIC methodology, MSA (Measurement System Analysis) addresses the Measure phase and process behavior charts (or control charts) address the Control phase. MSA helps you predict and characterize future outcomes. You can use the information gleaned from MSA to help you interpret and configure your process behavior charts.

For more information about Control Charts, see the “Control Chart Builder”.

Example of Measurement Systems Analysis

In this example, three operators measured the same five parts. See how the measurement system is performing, based on how much variation is found in the measurements.

1. Select Help > Sample Data Library and open Variability Data/Gasket.jmp.

2. Select Analyze > Quality and Process > Measurement Systems Analysis.

3. Assign Y to the Y, Response role.

4. Assign Part to the Part, Sample ID role.

5. Assign Operator to the X, Grouping role.

Notice that the MSA Method is set to EMP, the Chart Dispersion Type is set to Range, and the Model Type is set to Crossed. See Figure 7.5.

6. Click OK.

Figure 7.2 MSA Initial Report

The Average Chart shows the average measurements for each operator and part combination. In this example, the means of the part measurements are generally beyond the control limits. This is a desirable outcome, because it indicates that you can detect part-to-part variation.

The Range Chart shows the variability for each operator and part combination. In this example, the ranges are within the control limits. This is a desirable outcome, because it indicates that the operators are measuring parts in the same way and with similar variation.

The color coding for each part is shown in the legend below the charts.

7. From the red triangle menu next to Measurement Systems Analysis for Y, select Parallelism Plots.

Figure 7.3 Parallelism Plot for Operator and Part

The Parallelism Plots chart shows the average measurements for each part by operator. Because the lines are generally parallel and there is no major crossing, you conclude that there is no interaction between operators and parts.

Tip: Interactions indicate a serious issue that requires further investigation.

8. From the red triangle menu next to Measurement Systems Analysis for Y, select EMP Results.

Figure 7.4 EMP Results Report

The EMP Results report computes several statistics to help you assess and classify your measurement system. The Intraclass Correlation indicates the proportion of the total variation that you can attribute to the part.

From the EMP Results report, you can conclude the following:

• The Intraclass Correlation values are close to 1, indicating that most of the variation is coming from the part instead of the measurement system.

• The classification is First Class, meaning that the strength of the process signal is weakened by less than 11%.

• There is at least a 99% chance of detecting a warning using Test 1 only.

• There is 100% chance of detecting a warning using Tests 1-4.

Note: For more information about tests and detecting process shifts, see “Shift Detection Profiler”.

There is no interaction between operators and parts, and there is very little variation in your measurements (the classification is First Class). Therefore, you conclude that the measurement system is performing quite well.

Launch the Measurement Systems Analysis Platform

Launch the Measurement Systems Analysis platform by selecting Analyze > Quality and Process > Measurement Systems Analysis.

Figure 7.5 The Measurement Systems Analysis Window

The Measurement Systems Analysis window contains the following features:

Select Columns

lists all of the variables in your current data table. Move a selected column into a role.

MSA Method

select the method to use: EMP (Evaluating the Measurement Process) or Gauge R&R. This chapter covers the EMP method. For details about the Gauge R&R method, see the “Variability Gauge Charts” chapter.

Chart Dispersion Type

designates the type of chart for showing variation. Select the Range option or the Standard Deviation option.

Note: For the EMP method, the chart dispersion type determines how the statistics in the EMP Results report are calculated. If the Range option is selected, and you have a one factor or a two factor, balanced, crossed model, the statistics in this report are based on ranges. Otherwise, the statistics in this report are based on standard deviations.

Model Type

designates the model type:

‒ Main: variables with nominal or ordinal modeling types are treated as main effects.

‒ Crossed: the model is crossed when every level of every factor occurs with every level of every other factor.

‒ Crossed with Two Factor Interactions: the model is crossed when each level of two factors occurs with every level of the other factor.

‒ Nested: the model is nested when all levels of a factor appear within only a single level of any other factor.

‒ Cross then Nested (3 Factors Only): the factors are crossed and then nested for 3 factors.

‒ Nested then Crossed (3 Factors Only): the factors are nested and then crossed for 3 factors.

Options

contains the following options:

‒ Analysis Settings sets the REML maximum iterations and convergence.

‒ Specify Alpha specifies the 1-alpha confidence level.

Y, Response

is the column of measurements.

Part, Sample, ID

is the column designating the part or unit.

X, Grouping

is the column(s) representing grouping variables.

identifies a column that creates a report consisting of separate analyses for each level of the variable.

Measurement Systems Analysis Platform Options

Platform options appear within the red triangle menu next to Measurement Systems Analysis. Selecting an option creates the respective graph or report in the MSA report window. Deselecting an option removes the graph or report. Choose from the following options:

Average Chart

A plot of the average measurement values for each combination of the part and X variables. The Average Chart helps you detect product variation despite measurement variation. In an Average Chart, out of control data is desirable because it detects part-to-part variation. See “Average Chart”.

Range Chart

A plot of the variability statistic for each combination of the part and X variables. Appears only if you selected Range as the Chart Dispersion Type in the launch window. The Range Chart helps you check for consistency within subgroups. In a Range Chart, data within limits is desirable, indicating homogeneity in your error. See “Range Chart or Standard Deviation Chart”.

Std Dev Chart

A plot of the standard deviation statistic for each combination of the part and X variables. Appears only if you selected Standard Deviation as the Chart Dispersion Type in the launch window. The Standard Deviation Chart helps you check for consistency within subgroups. In a Standard Deviation Chart, data within limits is desirable, indicating homogeneity in your error. See “Range Chart or Standard Deviation Chart”.

Parallelism Plots

An overlay plot that reflects the average measurement values for each part. If the lines are relatively not parallel or crossing, there might be an interaction between the part and X variables.

Tip: Interactions indicate a serious issue that requires further investigation. For example, interactions between parts and operators mean that operators are measuring different parts differently, on average. Therefore, measurement variability is not predictable. This issue requires further investigation to find out why the operators do not have the same pattern or profile over the parts.

EMP Results

a report that computes several statistics to help you assess and classify your measurement system. See “EMP Results”.

Effective Resolution

a report containing results for the resolution of a measurement system. See “Effective Resolution”.

Bias Comparison

an Analysis of Means chart for testing if the X variables have different averages. See “Bias Comparison”.

Test-Retest Error Comparison

an Analysis of Means for Variances or Analysis of Means Ranges chart for testing if any of the groups have different test-retest error levels. See “Test-Retest Error Comparison”.

Shift Detection Profiler

an interactive set of charts that you can adjust to see the probabilities of getting warnings on your process behavior chart. See “Shift Detection Profiler”.

Variance Components

a report containing the estimates of the variance components for the given model. The calculations in this report are based on variances, not ranges. Balanced data uses the EMS method. Unbalanced data uses the REML method.

Note: This report is similar to the Variance Components report in the Variability Chart platform, except that it does not compute Bayesian variance component estimates. For more information, see “Variance Components” in the “Variability Gauge Charts” chapter.

EMP Gauge RR Results

a report that partitions the variability in the measurements into part variation and measurement system variation. The calculations in this report are based on variances, not ranges.

Note: This report is similar to the Gauge R&R report in the Variability Chart platform, except that the calculation for Reproducibility does not include interactions. For more information about Gauge R&R studies, see “About the Gauge R&R Method” in the “Variability Gauge Charts” chapter.

See the JMP Reports chapter in the Using JMP book for more information about the following options:

Local Data Filter

Shows or hides the local data filter that enables you to filter the data used in a specific report.

Redo

Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.

Save Script

Contains options that enable you to save a script that reproduces the report to several destinations.

Save By-Group Script

Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.

Average Chart

The red triangle menu next to Average Chart contains the following options:

Show Grand Mean

draws the overall mean of the Y variable on the chart.

Show Connected Means

draws lines connecting all of the average measurement values.

Show Control Limits

draws lines representing the Upper Control Limit (UCL) and the Lower Control Limit (LCL) and defines those values.

Show Control Limits Shading

adds shading between the UCL and LCL.

Show Separators

draws vertical lines to delineate between the X variables.

Show Data

adds the data points to the chart.

Note: You can replace variables in the Average Chart in one of two ways: swap existing variables by dragging and dropping a variable from one axis to the other axis; or, click on a variable in the Columns panel of the associated data table and drag it onto an axis.

Range Chart or Standard Deviation Chart

The red triangle menu next to Range Chart or Standard Deviation Chart contains the following options:

Show Average Dispersion

draws the average range or standard deviation on the chart.

Show Connected Points

draws lines connecting all of the ranges or standard deviations.

Show Control Limits

draws lines representing the Upper Control Limit (UCL) and the Lower Control Limit (LCL) and defines those values.

Show Control Limits Shading

adds shading between the UCL and LCL.

Show Separators

draws vertical lines to delineate between the X variables.

Note: You can replace variables in the Range or Standard Deviation Charts in one of two ways: swap existing variables by dragging and dropping a variable from one axis to the other axis; or, click on a variable in the Columns panel of the associated data table and drag it onto an axis.

EMP Results

Note: The statistics in this report are based on ranges in the following instances: if you selected EMP as the MSA Method and Range as the Chart Dispersion Type, and you have a one factor or a two factor, balanced, crossed model. Otherwise, the statistics in this report are based on variances.

The EMP Results report computes several statistics to help you assess and classify your measurement system. Using this report, you can determine the following:

• How your process chart is affected.

• Which tests to set.

• How much the process signal is attenuated.

• How much the bias factors are affecting your system and reducing your potential intraclass correlation coefficient.

The EMP Results report contains the following calculations:

Test-Retest Error

indicates measurement variation or repeatability (also known as within error or pure error).

Degrees of Freedom

indicates the amount of information used to estimate the within error.

Probable Error

the median error for a single measurement. Indicates the resolution quality of your measurement and helps you decide how many digits to use when recording measurements. For more information, see “Effective Resolution”.

Intraclass Correlation

indicates the proportion of the total variation that you can attribute to the part. If you have very little measurement variation, this number is closer to 1.

‒ Intraclass Correlation (no bias) does not take bias or interaction factors into account when calculating the results.

‒ Intraclass Correlation (with bias) takes the bias factors (such as operator, instrument, and so on) into account when calculating the results.

‒ Intraclass Correlation (with bias and interaction) takes the bias and interaction factors into account when calculating the results. This calculation appears only if the model is crossed and uses standard deviation instead of range.

Bias Impact

the amount by which the bias factors reduce the Intraclass Correlation.

Bias and Interaction Impact

the amount by which the bias and interaction factors reduce the Intraclass Correlation. This calculation appears only if the model is crossed and uses standard deviation instead of range.

Classes of Process Monitors

In order to understand the System and Classification parameters, you must first understand the Monitor Classification Legend.

Figure 7.6 Monitor Classification Legend

This legend describes the following classifications: First, Second, Third, and Fourth Class. Each classification indicates the following:

• the corresponding Intraclass Correlation values

• the amount of process signal attenuation (decrease)

• the chance of detecting a 3 standard error shift within 10 subgroups, using Wheeler’s test one or all four tests

Wheeler (2006) identifies four detection tests known as the Western Electric Zone Tests. Within the Shift Detection Profiler, there are eight tests that you can select from. The tests that correspond to the Wheeler tests are the first, second, fifth, and sixth tests.

Tip: To prevent the legend from appearing, deselect Show Monitor Classification Legend in the EMP Measurement Systems Analysis platform preferences.

Effective Resolution

The Effective Resolution report helps you determine how well your measurement increments are working. You might find that you need to add or drop digits when recording your measurements, or your current increments might be effective as is. Note the following:

• The Probable Error calculates the median error of a measurement.

• The Current Measurement Increment reflects how many digits you are currently rounding to and is taken from the data as the nearest power of ten. This number is compared to the Smallest Effective Increment, Lower Bound Increment, and Largest Effective Increment. Based on that comparison, a recommendation is made.

• Large measurement increments have less uncertainty in the last digit, but large median errors. Small measurement increments have small median errors, but more uncertainty in the last digit.

Shift Detection Profiler

Use the Shift Detection Profiler to assess the sensitivity of the control chart that you use to monitor your process. The Shift Detection Profiler estimates the probability of detecting shifts in the product mean or product standard deviation. The control chart limits include sources of measurement error variation. Based on these limits, the Shift Detection Profiler estimates the Probability of Warning. This is the probability that a control chart monitoring the process mean signals a warning over the next k subgroups.

You can set the subgroup size that you want to use for your control chart. Note the following:

• If the Subgroup Size equals one, the control chart is an Individual Measurement chart.

• If the Subgroup Size exceeds one, the control chart is an X-bar chart.

You can explore the effect of Subgroup Size on the control chart’s sensitivity. You can also explore the benefits of reducing bias and test-retest error.

Figure 7.7 shows the Shift Detection Profiler report for the Gasket.jmp sample data table, found in the Variability Data folder.

Figure 7.7 Shift Detection Profiler for Gasket.jmp

Probability of Warning

The Probability of Warning is the probability of detecting a change in the process. A change is defined by the Part Mean Shift and the Part Std Dev settings in the Shift Detection Profiler. The probability calculation assumes that the tests selected in the Customize and Select Tests outline are applied to the Number of Subgroups specified in the Profiler.

The control limits for the Individual Measurement chart (Subgroup Size = 1) and the X-bar chart (Subgroup Size > 1) are based on the In-Control Chart Sigma. The In-Control Sigma takes into account the bias factor (reproducibility) variation and the test-retest (repeatability) variation. These are initially set to the values obtained from your MSA study. The In-Control Chart Sigma also incorporates the In-Control Part Std Dev. Both of these values appear beneath the profiler, along with the False Alarm Probability, which is based on the In-Control Chart Sigma.

In-Control Part Std Dev

The standard deviation for the true part values, exclusive of measurement errors, for the stable process. The default value for In-Control Part Std Dev is the standard deviation of the part component estimated by the MSA analysis and found in the Variance Components report.

Often, parts for an MSA study are chosen to have specific properties and do not necessarily reflect the part-to-part variation seen in production. For this reason, you can specify the in-control part standard deviation by selecting Change In-Control Part Std Dev from the Shift Detection Profiler red triangle menu.

In-Control Chart Sigma

The value of sigma used to compute control limits. This value is computed using the In-Control Part Std Dev, the Bias Factors Std Dev, and Test-Retest Std Dev specified in the Shift Detection Profiler, and the Subgroup Size. The reproducibility factors are assumed to be constant within a subgroup.

For a subgroup of size n, control limits are set at the following values:

It follows that the In-Control Chart Sigma is the square root of the sum of the squares of the following terms:

‒ In-Control Part Std Dev

‒ Bias Factors Std Dev, as specified in the Shift Detection Profiler, multiplied by

‒ Test-Retest Std Dev, as specified in the Shift Detection Profiler

The Bias Factors Std Dev is multiplied by

to account for the assumption that the reproducibility factors are constant within a subgroup.

JMP updates the In-Control Chart Sigma when you change the In-Control Part Std Dev, the Bias Factors Std Dev, the Test-Retest Std Dev, or the Subgroup Size.

False Alarm Probability

The probability that the control chart tests signal a warning when no change in the part mean or standard deviation has occurred. JMP updates the False Alarm Probability when you change the Number of Subgroups or the tests in Customize and Select Tests.

For more information about the Variance Components report, see “Variance Components” in the “Variability Gauge Charts” chapter.

Shift Detection Profiler Settings

Number of Subgroups

The number of subgroups over which the probability of a warning is computed. If the number of subgroups is set to k, the profiler gives the probability that the control chart signals at least one warning based on these k subgroups. The Number of Subgroups is set to 10 by default. Drag the vertical line in the plot to change the Number of Subgroups.

Part Mean Shift

The shift in the part mean. By default, the profiler is set to detect a 1 sigma shift. The initial value is the standard deviation of the part component estimated by the MSA analysis and found in the Variance Components report. Drag the vertical line in the plot or click the value beneath the plot to change the Part Mean Shift.

Part Std Dev

The standard deviation for the true part values, exclusive of measurement errors. The initial value for Part Std Dev is the standard deviation of the part component estimated by the MSA analysis and is found in the Variance Components report. Drag the vertical line in the plot or click the value beneath the plot to change the Part Std Dev.

Bias Factors Std Dev

The standard deviation of factors related to reproducibility. Bias factors include operator and instrument. The bias factor variation does not include part and repeatability (within) variation. The initial value is derived using the reproducibility and interaction variance components estimated by the MSA analysis and is found in the Variance Components report. Drag the vertical line in the plot or click the value beneath the plot to change the Bias Factors Std Dev.

Test-Retest Std Dev

The standard deviation of the test-retest, or repeatability, variation in the model. The initial value is the standard deviation of the Within component estimated by the MSA analysis and is found in the Variance Components report. Drag the vertical line in the plot or click the value beneath the plot to change the Test-Retest Std Dev.

Subgroup Size

The sample size used for each subgroup. This is set to 1 by default. You can increase the sample size to investigate improvement in control chart performance. Increasing the sample size from 1 demonstrates what happens when you move from an Individual Measurement chart to an XBar chart. Drag the vertical line in the plot to change the Subgroup Size.

Shift Detection Profiler Options

The red triangle menu for the Shift Detection Profiler provides several options. Only one option is described here.

Change In-Control Part Std Dev

Specify a value for the part standard deviation for the stable process. The in-control part standard deviation should reflect the variation of the true part values, exclusive of measurement errors. Enter a new value and click OK.

The In-Control Part Std Dev is originally set to the standard deviation of the part component estimated by the MSA analysis, found in the Variance Components report.

This option is useful if the parts chosen for the EMP study were not a random sample from the process.

Reset Factor Grid

Displays a window for each factor allowing you to enter a specific value for the factor’s current setting, to lock that setting, and to control aspects of the grid. See the Introduction to Profilers chapter in the Profilers book for details.

Factor Settings

Submenu that consists of the following options:

Remember Settings

Adds an outline node to the report that accumulates the values of the current settings each time the Remember Settings command is invoked. Each remembered setting is preceded by a radio button that is used to reset to those settings.

Copy Settings Script

Copies the current Profiler’s settings to the clipboard.

Paste Settings Script

Pastes the Profiler settings from the clipboard to a Profiler in another report.

Set Script

Sets a script that is called each time a factor changes. The set script receives a list of arguments of the form:

{factor1 = n1, factor2 = n2, ...}

For example, to write this list to the log, first define a function:

ProfileCallbackLog = Function({arg},show(arg));

Then enter ProfileCallbackLog in the Set Script dialog.

Similar functions convert the factor values to global values:

ProfileCallbackAssign = Function({arg},evalList(arg));

Or access the values one at a time:

ProfileCallbackAccess = Function({arg},f1=arg["factor1"];f2=arg["factor2"]);

Shift Detection Profiler Legend

This panel gives a brief description of four of the Shift Detection Profiler settings. For further details, see “Shift Detection Profiler Settings”.

Tip: To prevent the legend from appearing, deselect Show Shift Detection Profiler Legend in the EMP Measurement Systems Analysis platform preferences.

Customize and Select Tests

In the Customize and Select Tests panel, select and customize the tests that you want to apply to the k subgroups in your control chart. The eight tests are based on Nelson (1984). For more details about the tests, see “Tests” in the “Control Chart Builder” chapter.

The Shift Detection Profiler calculations take these tests into account. The Probability of Warning and False Alarm Probability values increase as you add more tests. Because the calculations are based on a quasi-random simulation, there might be a slight delay as the profiler is updated.

The Customize and Select Tests panel has the following options:

Restore Default Settings

If no settings have been saved to preferences, this option resets the selected tests to the first test only. The values of n are also reset to the values described in “Tests” in the “Control Chart Builder” chapter. If settings have been saved to preferences, this option resets the selected tests and the values of n to those specified in the preferences.

Note: You can access preferences for control chart tests by selecting File > Preferences> Platforms > Control Chart Builder. Custom Tests 1 through 8 correspond to the eight tests shown in Customize and Select Tests.

Save Settings to Preferences

Saves the selected tests and the values of n for use in future analyses. These preferences are added to the Control Chart Builder platform preferences.

Bias Comparison

The Bias Comparison option creates an Analysis of Means chart. This chart shows the mean values for each level of the grouping variables and compares them with the overall mean. You can use this chart to see whether an operator is measuring parts too high or too low, on average.

The red triangle menu next to Analysis of Means contains the following options:

Set Alpha Level

select an option from the most common alpha levels or specify any level using the Other selection. Changing the alpha level modifies the upper and lower decision limits.

Show Summary Report

shows a report containing group means and decision limits, and reports if the group mean is above the upper decision limit or below the lower decision limit.

Display Options

include the following options:

‒ Show Decision Limits draws lines representing the Upper Decision Limit (UDL) and the Lower Decision Limit (LDL) and defines those values.

‒ Show Decision Limit Shading adds shading between the UDL and the LDL.

‒ Show Center Line draws the center line statistic that represents the average.

‒ Point Options changes the chart display to needles, connected points, or points.

Test-Retest Error Comparison

The Test-Retest Error Comparison option creates a type of Analysis of Means for Variances or Analysis of Means Ranges chart. This chart shows if there are differences in the test-retest error between operators. For example, you can use this chart to see whether there is an inconsistency in how each operator is measuring. The Analysis of Mean Ranges chart is displayed when ranges are used for variance components.

• For information about the options in the red triangle menu next to Operator Variance Test, see “Bias Comparison”.

• For more information about Analysis of Means for Variances charts, see “Variance Components” in the “Variability Gauge Charts” chapter.

Additional Example of Measurement Systems Analysis

In this example, three operators have measured a single characteristic twice on each of six wafers. Perform a detailed analysis to find out how well the measurement system is performing.

Perform the Initial Analysis

1. Select Help > Sample Data Library and open Variability Data/Wafer.jmp.

2. Select Analyze > Quality and Process > Measurement Systems Analysis.

3. Assign Y to the Y, Response role.

4. Assign Wafer to the Part, Sample ID role.

5. Assign Operator to the X, Grouping role.

Notice that the MSA Method is set to EMP, the Chart Dispersion Type is set to Range, and the Model Type is set to Crossed.

6. Click OK.

Figure 7.8 Average and Range Charts

The Average Chart shows that some of the average part measurements fall beyond the control limits. This is desirable, indicating measurable part-to-part variation.

The Range Chart shows no points that fall beyond the control limits. This is desirable, indicating that the operator measurements are consistent within part.

Examine Interactions

Take a closer look for interactions between operators and parts. From the red triangle menu next to Measurement Systems Analysis for Y, select Parallelism Plots.

Figure 7.9 Parallelism Plot

Looking at the parallelism plot by operator, you can see that the lines are relatively parallel and that there is only some minor crossing.

Examine Operator Consistency

Take a closer look at the variance between operators. From the red triangle menu next to Measurement Systems Analysis for Y, select Test-Retest Error Comparison.

Figure 7.10 Test-Retest Error Comparison

Looking at the Test-Retest Error Comparison, you can see that none of the operators have a test-retest error that is significantly different from the overall test-retest error. The operators appear to be measuring consistently.

Just to be sure, you decide to look at the Bias Comparison chart, which indicates whether an operator is measuring parts too high or too low. From the red triangle menu next to Measurement Systems Analysis for Y, select Bias Comparison.

Figure 7.11 Bias Comparison

Looking at the Bias Comparison chart, you make the following observations:

• Operator A and Operator B have detectable measurement bias, as they are significantly different from the overall average.

• Operator A is significantly biased low.

• Operator B is significantly biased high.

• Operator C is not significantly different from the overall average.

Classify Your Measurement System

Examine the EMP Results report to classify your measurement system and look for opportunities for improvement. From the red triangle menu next to Measurement Systems Analysis for Y, select EMP Results.

Figure 7.12 EMP Results

The classification is Second Class, which means that there is a better than 88% chance of detecting a three standard error shift within ten subgroups, using Test one only. You notice that the bias factors have an 11% impact on the Intraclass Correlation. In other words, if you could eliminate the bias factors, your Intraclass Correlation coefficient would improve by 11%.

Explore the Ability of a Control Chart to Detect Process Changes

Use the Shift Detection Profiler to explore the probability that a control chart will be able to detect a change in your process. From the red triangle menu next to Measurement Systems Analysis for Y, select Shift Detection Profiler.

Figure 7.13 Shift Detection Profiler

By default, the only test selected is for a point beyond the 3 sigma limits. Also note that the default Subgroup Size is 1, indicating that you are using an Individual Measurement chart.

Explore your ability to detect a shift in the mean of two part standard deviations in the 10 subgroups following the shift. Click the Part Mean Shift value of 2.1701 and change it to 4.34 (2.17 multiplied by 2). The probability of detecting a shift of twice the part standard deviation is 56.9%.

Next, see how eliminating bias affects your ability to detect the shift of two part standard deviations. Change the Bias Factors Std Dev value from 1.1256 to 0. The probability of detecting the shift increases to 67.8%.

Finally, add more tests to see how your ability to detect the two part standard deviation shift changes. In addition to the first test, select the second, fifth, and sixth tests (Wheeler’s Rules 4, 2, and 3). With these four tests and no bias variation, your probability of detecting the shift is 99.9%.

You can also explore the effect of using a control chart based on larger subgroup sizes. For subgroup sizes of two or more, the control chart is an X-bar chart. Change the Bias Factors Std Dev value back to 1.1256 and deselect all but the first test. Set the Subgroup Size in the profiler to 4. The probability of detecting the two part standard deviation shift is 98.5%.

Examine Measurement Increments

Finally, see how well your measurement increments are working. From the red triangle menu next to Measurement Systems Analysis for Y, select Effective Resolution.

Figure 7.14 Effective Resolution

The Current Measurement Increment of 0.01 is below the Lower Bound Increment of 0.09, indicating that you should adjust your future measurements to record one less digit.

Statistical Details for Measurement Systems Analysis

Intraclass Correlation without bias is computed as follows: