MSA - Measurement Systems Analysis

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MSA - Measurement Systems Analysis

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<ul><li> 1. CONTENTSINDEX MEET MTB UGUIDE 1 UGUIDE 2SC QREF HOW TO USE 11 Measurement Systems AnalysisMeasurement Systems Analysis Overview, 11-2 sGage R&amp;R Study, 11-4 sGage Run Chart, 11-23 sGage Linearity and Accuracy Study, 11-27 s MINITAB Users Guide 211-1CONTENTSINDEX MEET MTB UGUIDE 1 UGUIDE 2SC QREF HOW TO USE </li></ul><p> 2. CONTENTS INDEX MEET MTB UGUIDE 1 UGUIDE 2 SC QREF HOW TO USEChapter 11 Measurement Systems Analysis Overview Measurement Systems Analysis Overview MINITAB offers several commands to help you determine how much of your process variation arises from variation in your measurement system.Gage R&amp;R (Crossed), Gage R&amp;R (Nested), and Gage Run Chart examine s measurement system precision.Gage Linearity and Accuracy examines gage linearity and accuracy. sAny time you measure the results of a process you will see some variation. This variation comes from two sources: one, there are always differences between parts made by any process, and two, any method of taking measurements is imperfectthus, measuring the same part repeatedly does not result in identical measurements. Statistical Process Control (SPC) is concerned with identifying sources of part-to-part variation, and reducing that variation as much as possible to get a more consistent product. But before you do any SPC analyses, you may want to check that the variation you observe is not overly due to errors in your measurement system.Measurement system error Measurement system errors can be classified into two categories: accuracy and precision.Accuracy describes the difference between the measurement and the parts actual s value.Precision describes the variation you see when you measure the same part repeatedly s with the same device. Within any measurement system, you can have one or both of these problems. For example, you can have a device which measures parts precisely (little variation in the measurements) but not accurately. You can also have a device that is accurate (the average of the measurements is very close to the accurate value), but not precise, that is, the measurements have large variance. You can also have a device that is neither accurate nor precise. accurate and precise precise but not accurate accurate but not precisenot accurate or precise 11-2MINITAB Users Guide 2CONTENTS INDEX MEET MTB UGUIDE 1 UGUIDE 2 SC QREF HOW TO USE 3. CONTENTSINDEXMEET MTBUGUIDE 1 UGUIDE 2 SC QREFHOW TO USEMeasurement Systems Analysis OverviewMeasurement Systems Analysis Accuracy The accuracy of a measurement system is usually broken into three components:linearitya measure of how the size of the part affects the accuracy of the s measurement system. It is the difference in the observed accuracy values through theexpected range of measurements.accuracya measure of the bias in the measurement system. It is the difference s between the observed average measurement and a master value.stabilitya measure of how accurately the system performs over time. It is the total s variation obtained with a particular device, on the same part, when measuring asingle characteristic over time. To examine your measurement systems accuracy, see Gage Linearity and Accuracy Study on page 11-27.Precision Precision, or measurement variation, can be broken down into two components:repeatabilitythe variation due to the measuring device. It is the variation observed s when the same operator measures the same part repeatedly with the same device.reproducibilitythe variation due to the measurement system. It is the variation s observed when different operators measure the same parts using the same device. To examine your measurement systems precision, see Gage R&amp;R Study on page 11-4. To look at a plot of all of the measurements by operator/part combination, and thus visualize the repeatability and reproducibility components of the measurement variation, see Gage Run Chart on page 11-23. Data sets used in examples The same two data sets are used in the Gage R&amp;R (Crossed) Study and the Gage Run Chart examples:GAGE2.MTW, in which measurement system variation has a large effect on the s overall observed variationGAGEAIAG.MTW, in which measurement system variation has a small effect on the s overall observed variation You can compare the output for the two data sets, as well as compare results from the various analyses. The Gage Linearity and Accuracy Study example uses the GAGELIN.MTW data set. GAGEAIAG.MTW and GAGELIN.MTW are reprinted with permission from the Measurement Systems Analysis Reference Manual (Chrysler, Ford, General Motors Supplier Quality Requirements Task Force).MINITAB Users Guide 2 11-3CONTENTSINDEXMEET MTBUGUIDE 1 UGUIDE 2 SC QREFHOW TO USE 4. CONTENTS INDEXMEET MTBUGUIDE 1UGUIDE 2SC QREFHOW TO USEChapter 11 Gage R&amp;R Study Gage R&amp;R Study Gage repeatability and reproducibility studies determine how much of your observed process variation is due to measurement system variation. MINITAB allows you to perform either crossed or nested Gage R&amp;R studies. Use Gage R&amp;R Study (Crossed) when each part is measured multiple times by each soperator. Use Gage R&amp;R Study (Nested) when each part is measured by only one operator, ssuch as in destructive testing. In destructive testing, the measured characteristic is different after the measurement process than it was at the beginning. Crash testing is an example of destructive testing.MINITAB provides two methods for assessing repeatability and reproducibility: X and R, and ANOVA. The X and R method breaks down the overall variation into three categories: part-to-part, repeatability, and reproducibility. The ANOVA method goes one step further and breaks down reproducibility into its operator, and operator-by-part, components.Overall Variation Measurement System VariationPart-to-Part VariationVariation due toVariation due to gageReproducibilitRepeatabilit OperatorOperator by The ANOVA method is more accurate than the X and R method, in part, because it considers the operator by part interaction [3] and [4]. Gage R&amp;R Study (Crossed) allows you to choose between the X and R method and the ANOVA method. Gage R&amp;R Study (Nested) uses the ANOVA method only. If you need to use destructive testing, you must be able to assume that all parts within a single batch are identical enough to claim that they are the same part. If you are unable to make that assumption then part-to-part variation within a batch will mask the measurement system variation. If you can make that assumption, then choosing between a crossed or nested Gage R&amp;R Study for destructive testing depends on how your measurement process is set up. If all 11-4MINITAB Users Guide 2CONTENTS INDEXMEET MTBUGUIDE 1UGUIDE 2SC QREFHOW TO USE 5. CONTENTSINDEX MEET MTBUGUIDE 1UGUIDE 2 SC QREFHOW TO USEGage R&amp;R Study Measurement Systems Analysis operators measure parts from each batch, then use Gage R&amp;R Study (Crossed). If each batch is only measured by a single operator, then you must use Gage R&amp;R Study (Nested). In fact, whenever operators measure unique parts, you have a nested design.DataGage R&amp;R Study (Crossed) Structure your data so that each row contains the part name or number, operator (optional), and the observed measurement. Parts and operators can be text or numbers.PartNum OperatorMeasure 1Daryl1.48 1Daryl1.43 2Daryl1.83 2Daryl1.83 3Daryl1.53 3Daryl1.38 1 Beth 1.78 1 Beth 1.33 The Gage R&amp;R studies require balanced designs (equal numbers of observations per cell) and replicates. You can estimate any missing observations with the methods described in [2].Gage R&amp;R Study (Nested) Structure your data so that each row contains the part name or number, operator, and the observed measurement. Parts and operators can be text or numbers. Part is nested within operator, because each operator measures unique parts. NoteIf you use destructive testing, you must be able to assume that all parts within a singlebatch are identical enough to claim that they are the same part. MINITAB Users Guide 2 11-5CONTENTSINDEX MEET MTBUGUIDE 1UGUIDE 2 SC QREFHOW TO USE 6. CONTENTS INDEXMEET MTB UGUIDE 1 UGUIDE 2SC QREF HOW TO USEChapter 11 Gage R&amp;R StudyIn the example on the right, PartNum1 for Daryl is truly a different part from PartNum1 for Beth.PartNumOperator Measure PartNum OperatorMeasure 1Daryl1.481 Daryl 1.48 1Daryl1.431 Daryl 1.43 2Daryl1.832 Daryl 1.83 2Daryl1.832 Daryl 1.83 3Daryl1.533 Daryl 1.53 3Daryl1.523 Daryl 1.52 4 Beth 1.38 1Beth 1.38 4 Beth 1.78 1Beth 1.78 5 Beth 1.33 2Beth 1.33 The Gage R&amp;R studies require balanced designs (equal numbers of observations per cell) and replicates. You can estimate any missing observations with the methods described in [2]. h To do a Gage R&amp;R Study (Crossed)1 Choose Stat Quality Tools Gage R&amp;R Study (Crossed). 2 In Part numbers, enter the column of part names or numbers.3 In Measurement data, enter the column of measurements.4 If you like, use any of the options described below, then click OK. 11-6MINITAB Users Guide 2CONTENTS INDEXMEET MTB UGUIDE 1 UGUIDE 2SC QREF HOW TO USE 7. CONTENTSINDEXMEET MTB UGUIDE 1UGUIDE 2SC QREFHOW TO USEGage R&amp;R Study Measurement Systems Analysish To do a Gage R&amp;R Study (Nested)1 Choose Stat Quality Tools Gage R&amp;R Study (Nested). 2 In Part or batch numbers, enter the column of part or batch names or numbers.3 In Operators, enter the column of operator names or numbers.4 In Measurement data, enter the column of measurements.5 If you like, use any of the options described below, then click OK. OptionsGage R&amp;R Study dialog box(Gage R&amp;R (Crossed) only) add operators as a factor in the model s(Gage R&amp;R (Crossed) only) use the ANOVA or X and R (default) method of analysis sGage Info subdialog boxfill in the blank lines on the graphical output label sOptions subdialog boxchange the multiple in the Study Var (5.15SD) column by entering a study s variationsee StudyVar in Session window output on page 11-9display a column showing the percentage of process tolerance taken up by each s variance component (a measure of precision-to-tolerance for each component)display a column showing the percentage of process standard deviation taken up by s each variance componentchoose not to display percent contribution or percent study variation sdraw plots on separate pages, one plot per page sreplace the default graph title with your own title s MINITAB Users Guide 2 11-7CONTENTSINDEXMEET MTB UGUIDE 1UGUIDE 2SC QREFHOW TO USE 8. CONTENTSINDEXMEET MTBUGUIDE 1UGUIDE 2SC QREFHOW TO USEChapter 11 Gage R&amp;R StudyMethodGage R&amp;R Study (Crossed)X and R method MINITAB first calculates the sample ranges from each set of measurements taken by an operator on a part. The sample ranges are then used to calculate the average range for repeatability. The variance component for reproducibility is calculated from the range of the averages of all measurements for each operator. Reproducibility, in this case, is the same as the variance component for operator. The variance component for parts is calculated from the range of the averages of all measurements for each part. Note All ranges are divided by the appropriate d2 factor. ANOVA method When both Parts and Operators are entered When you enter Operators as well as Parts, your data are analyzed using a balanced two-factor factorial design. Both factors are considered to be random. The model includes the main effects of Parts and Operators, plus the Part by Operator interaction. (When operators are not entered, the model is a balanced one-way ANOVA with Part as a random factor, as described in the next section.) MINITAB first calculates the ANOVA table for the appropriate model. That table is then used to calculate the variance components, which appear in the Gage R&amp;R tables. Note Some of the variance components could be estimated as negative numbers when the Part by Operator term in the full model is not significant. MINITAB will first display an ANOVA table for the full model. If the p-value for the Part by Operator term is &gt; 0.25, a reduced model is then fitted and used to calculate the variance components. This reduced model includes only the main effects of Part and Operator. With the full model, the variance component for Reproducibility is further broken s down into variation due to Operator and variation due to the Part by Operatorinteraction: The Operator component is the variation observed between different operatorsmeasuring the same part. The Part by Operator interaction is the variation among the average part sizesmeasured by each operator. This interaction takes into account cases where, forinstance, one operator gets more variation when measuring smaller parts, whereasanother operator gets more variation when measuring larger parts.Use the table of variance components to interpret these effects.With the reduced model, the variance component for Reproducibility is simply the s variance component for Operator. 11-8MINITAB Users Guide 2CONTENTSINDEXMEET MTBUGUIDE 1UGUIDE 2SC QREFHOW TO USE 9. CONTENTSINDEX MEET MTBUGUIDE 1 UGUIDE 2 SC QREFHOW TO USEGage R&amp;R StudyMeasurement Systems Analysis When Operators are not entered When you only enter the parts, the model is a balanced one-way ANOVA, and Part is considered a random factor. MINITAB calculates the ANOVA table and estimates the variance components for Part and Gage. The variance component for Gage is the same as Repeatability, and no Reproducibility component is estimated. Thus, the variance component for Gage is the error term from the ANOVA model.MethodGage R&amp;R Study (Nested)ANOVA Method When you use Gage R&amp;R Study (Nested), your data are analyzed using a nested design. The model includes the main effects for Operator and Part (Operator), in which part is nested in operator. Because each operator measures distinct parts, there is no Operator-by-Part interaction. MINITAB first calculates the ANOVA table for the appropriate model. That table is then used to calculate the variance componentsRepeatability, Reproducibility, and Part-to-Part. NoteSome of the variance components could be estimated as negative numbers when thePart by Operator term in the full model is not significant. MINITAB will first display anANOVA table for the full model. If the p-value for the Part by Operator term is &gt; 0.25, areduced model is then fitted and used to calculate the variance components. Thisreduced model includes only the main effects of Part and Operator. Session window output The Session window output consists of several tables: ANOVA Table (ANOVA method only)displays the usual analysis of variance output sfor the fitted effects. See Note under ANOVA method on page 11-8 for more information. Gage R&amp;R s VarComp (or Variance)the variance component contributed by each source. %Contributionthe percent contribution to the overall variation made by each variance component. (Each variance component divided by the total variation, then multiplied by 100.) The percentages in this column add to 100. StdDevthe standard deviation for each variance component...</p>

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