Statistical Quality Analysis - Minitab

1 Assessing Measurement System VariationExample 1: Fuel Injector Nozzle DiametersProblemA manufacturer of fuel injector nozzles installs a new digitalmeasuring system. Investigators want to determine how wellthe new system measures the injector nozzle measuredNozzleData collectionTechnicians randomly sample, across all major sources ofprocess variation (machine, time, shift, job change), 9 nozzlesthat represent those that are typically produced. They codeOperator who measuredOperatorOriginal run order of the experimentRun OrderMeasured diameter of nozzle (microns)Diamthe nozzles to identify the measurements taken on first operator measures the 9 nozzles in random , the second operator measures the 9 nozzles in adifferent random order. Each operator repeats the processtwice, for a total of 36 valid measurement system analyses, you must randomlysample and measure specificationfor the nozzle diameters is 9012 4 tolerance is 8 Gage R&R Study (Crossed)Gage Studies for Continuous Data3 Assessing Measurement System Measurement systems analysisWhat is measurement systems analysisMeasurement systems Analysis assesses the adequacy of ameasurementsystem fora output from a process, consider two sources of variation:Why use measurement systems analysisMeasurement systems Analysis answers questions such as: Canthemeasurementsystemadequatelydiscrim inatebetweendifferent parts?

2 Part-to-part variation Is the measurement system stable over time? Measurement system variation Is the measurement system accurate throughout the range ofparts?If measurement system variation is large compared topart-to-part variation, the measurements may not provideuseful example: Can a viscometer adequately discriminate betweentheviscosityof several paint samples?When to use measurement systems analysisBefore you collect data from your process (for example, toanalyze process control or capability), use measurementsystem Analysis to confirm that the measurement system Does a scale need to be periodically recalibrated to accuratelymeasure the fill weight of bags of potato chips?measures consistently and accurately, and adequatelydiscriminates between parts. Does a thermometer accurately measure the temperature forall heat settings that are used in the process?

3 Gage Studies for Continuous Data4 Assessing Measurement System Gage R&R study (crossed)What is a gage R&R study (crossed)A crossed gage R&R study estimates how much total processvariation is caused by the measurement system. Total processvariation consists of part-to-part variation plus measurementsystem variation. Measurement system variation consists of:Why use a gage R&R study (crossed)Thisstudycomparesmeasurementsys temvariationtototalprocessvariation or tolerance. If the measurement system variation is largein proportion to total variation, the system may not adequatelydistinguish between parts. Repeatability variation due to the measuring device, orthe variation observed when the same operator measuresthe same part repeatedly with the same deviceA crossed gage R&R study can answer questions such as: Is the variability of a measurement system small comparedwith the manufacturing process variability?

4 Reproducibility variation due to the measuring system,orthevariationobservedwhendiffere ntoperatorsmeasurethe same part using the same device Is the variability of a measurement system small comparedwith the process specification limits? How much variability in a measurement system is caused bydifferences between operators?When you estimate repeatability, each operator measureseach part at least twice. When you estimate reproducibility,at least two operators must measure the parts. Operators Is a measurement system capable of discriminating betweenparts?measure the parts in random order, and the selected partsrepresent the possible range of example:When to use a gage R&R study (crossed) Use gage R&R to evaluate a measurement system beforeusing it to monitor or improve a process. How much of the variability in the measured diameter of abearing is caused by the caliper?

5 How much of the variability in the measured diameter of abearing is caused by the operator? Use the crossed Analysis when each operator measureseach part (or batch, for a destructive test) multiple times. Can the measurement system discriminate between bearingsof different size?Gage Studies for Continuous Data5 Assessing Measurement System Measurement system errorMeasurement system errors can be classified into twocategories:AccuracyThe accuracy of a measurement system has three components: Accuracy the difference between the part s measuredand actual value Bias a measure of the inaccuracyin the measurement system;the difference between the observed average measurementand a master value Precision the variation when the same part is measuredrepeatedly with the same device Linearity a measure of how the size of the part affects thebias of the measurement system; the difference in the observedbias values through the expected range of measurementsErrors of one or both of these categories may occur withinany measurementsystem.

6 For example,a devicemay measureparts precisely (little variation in the measurements) but not Stability a measure of how well the system performs overtime; the total variation obtained with a particular device, onthe same part, when measuring a single characteristic overtimeaccurately. Or a device may be accurate (the average of themeasurements is very close to the master value), but notprecise (the measurements have large variance). Or a devicemay be neither accurate nor , or measurement variation, has two components:accurate andpreciseinaccurate butpreciseaccurate butimpreciseinaccurate andimprecise Repeatability variation due to the measuring device, or thevariationobservedwhenthesameoperatorm easuresthesamepart repeatedly with the same device Reproducibility variation due to the measuring system, or thevariationobserved when different operators measure the samepart using the same deviceGage Studies for Continuous Data6 Assessing Measurement System Assessing the measurement systemUse a Gage R&R study (crossed) to assess:Gage R&R Study (Crossed)1.

7 Open How well the measuring system can distinguish betweenparts2. ChooseStat> Quality Tools>Gage Study>Gage R&RStudy (Crossed). Whether the operators measure consistently3. Complete the dialog box as shown specification limits for the nozzle diameters are 9012 4microns. In other words, the nozzle diameter is allowed tovary by as much as 4 microns in either direction. The toleranceis the difference between the specification limits: 9016 9008= 8 entering a value inProcess tolerance, you can estimatewhat proportion of the tolerance is taken up by the variationin the measurement UnderProcess tolerance, chooseUpper spec - Lower specand CheckDrawgraphsonseparategraphs, ClickOKin each dialog Studies for Continuous Data7 Assessing Measurement System Interpreting your resultsAnalysis of variance tablesMinitab uses the Analysis of variance (ANOVA) procedure tocalculate variance components, and then uses thosecomponents to estimate the percent variation due to themeasuring system.

8 The percent variation appears in the gageR&R tableincludesterms forthepart(Nozzle),operator (Operator), and operator-by-part interaction(Nozzle*Operator).If the p-value for the operator-by-part interaction is , Minitab generates a second ANOVA table that omits theinteraction term from the model. To alter the default Type Ierror rate of , clickOptionsin the main dialog box. InAlpha to remove interaction term, type a new value (forexample, ).Here, the p-value for Nozzle*Operator is Therefore, Minitab removes the interaction term from the model andgenerates a second ANOVA Studies for Continuous Data8 Assessing Measurement System Interpreting your resultsVariance componentsMinitab also calculates a column of variance components(VarComp) and uses the values to calculate %Contributionwith the ANOVA variance components table breaks down the sources oftotal variability: Total Gage R&Rconsists of: Repeatability the variability from repeatedmeasurements by the sameoperator.

9 Reproducibility the variability when the same partis measured by different operators. (This can be furtherdivided into operator and operator-by-partcomponents.) Part-To-Part the variability in measurements acrossdifferent use variance components?Use variance components to assess the amount of variationthat each source of measurement error and the part-to-partdifferences contribute to the total , differences between parts should account for most ofthe variability; variability from repeatability and reproducibilityshould be very Studies for Continuous Data9 Assessing Measurement System Interpreting your resultsPercent contribution%Contribution is based on the estimates of the variancecomponents. Each value in VarComp is divided by the TotalVariation, and then multiplied by example, to calculate the %Contribution for Part-to-Part,divide the VarComp for Part-to-Part by the Total Variationand multiply by 100:( ) * 100 , of the total variation in the measurementsis due to the differences between parts.

10 This high% Part-to-Part is high, the system can distinguish variance versus standard deviationBecause %Contribution is based on the total variance, thecolumn of values adds up to 100%. Minitab also displays columns with percentages based on thestandard deviation of each term. These columns, labeled%StudyVar and %Tolerance, typically do not add up to 100%.Because the standard deviation uses the same units as thepart measurements and the tolerance,it allows for Studies for Continuous Data10 Assessing Measurement System Interpreting your resultsPercent study variationUse %StudyVar to compare themeasurementsystem variationto the total calculates %StudyVar by dividing each value inStudyVar by Total Variation and then multiplying by for gage R&R is( ) * 100 calculates StudyVar as 6 times the standard deviationfor each process variationTypically, process variation is defined as 6s, where s is thestandard deviation, as an estimate of.