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Measurement ErrorBefore we do any experiments, collect any data, or set upany process: We need to ensure we have a way to measurethe results that is:QuantitativeAccuratePreciseSo how do we test our measurement system or gage to ensurethis?1/24/03Measurement error 21

Measurement Tool ( Gage) Error1/24/03Measurement error 22

Measurement ErrorMeasurement Error will always exist. The idea is to measure and minimize thisinherent measurement tool measuring error so that it can measure “real”differences in the “process” intended or due to some other unwanted assignablecause.1/24/03Measurement error 23

Types of Measurement ErrorStatistical Treatment of DataLow accuracy, low precisionLow accuracy, high precision1/24/03High accuracy, low precisionHigh accuracy, high precisionMeasurement error 24

Types of Measurement Error Terms:Accuracy1/24/03Measurement error 25

Types of Measurement Error Terms:Repeatability1/24/03Measurement error 26

Types of Measurement Error Terms:Repeatability1/24/03Measurement error 27

Types of Measurement Error Terms:Reproducibility1/24/03Measurement error 28

Types of Measurement Error Terms:Reproducibility1/24/03Measurement error 29

Types of Measurement Error Terms:Stability1/24/03Measurement error 210

Measurement Error Analysis:Accuracy and Stability Example1/24/03Measurement error 211

Method to Quantify Measurement ErrorsAnalysisI. Gage R&R Study : Reproducibility and Repeatability:Methods of analysis:Average and range.II. ISOPLOT : Repeated Measurement StudyMeasure same parts twiceT test and F test for difference between measurementsystems1/24/03Measurement error 212

Measurement Tool ( Gage) Error; Precision toTolerance ideas: P/T ratioRules for measurement system discrimination of a processchange: Typical units of measure are a ratio P/T (precisionto tolerance):At least 1/10 of 6 sigma of process variationOther: at least 1/10 of process tolerance (spec limits).1/24/03Measurement error 213

Measurement Tool ( Gage) Error; Precision toTolerance ideas: P/T ratio1/24/03Measurement error 214

Measurement Tool ( Gage) Error; Precision toTolerance ideas: Repeatability andReproducibility (R&R) Study1/24/03Measurement error 215

Measurement Tool ( Gage) Error; Precision toTolerance ideas: Repeatability andReproducibility (R&R) Study1/24/03Measurement error 216

Measurement Tool ( Gage) Error; Precision to Toleranceideas: Repeatability and Reproducibility (R&R) StudyI. To evaluate the measurement systems capability,we form aratio comparing the gage R&R to the tolerance width (spec width) as:%R&R as Precision to Tolerance 6σR&R/(USL-LSL)II. Or a ratio comparing the gage R&R to the total processvariation as:%R&R as Precision to Total Variation 6σR&R/ 6σtotal variationSome ratios some 5.15 x sigma instead of 6.00 as:5.15σ 99% of the data for normal distribution6.00σ 99.7% of the data for normal distribution1/24/03Measurement error 217

Measurement Tool ( Gage) Error; Precision to Toleranceideas: Repeatability and Reproducibility (R&R) StudyΙ.σR&R RRS :(Sqrt(σ2repeatability x σ2reproducibility)II. Estimate of σ repeatability (Average Range ofmeasurements)/d2III. Estimate of σreproducibility Sqrt[(average difference/d2)2 – (σ2repeat/(#parts x #trials)]IV. Total Variation TV sqrt[(6σR&R)2 (6σprocess variation )2 ]1/24/03Measurement error 218

Measurement Tool ( Gage) Error; Precision to Toleranceideas: Repeatability and Reproducibility (R&R) StudyThe d2 term is used to estimate σ for small sample sizes (comesfrom a table:1/24/03Measurement error 219

Isoplot supposed a Copyrighted name by Dorian Shainin :Very similar to the R&R gage AnalysisMeasurement systems require a discrimination ratio or Signalto noise ratio of 6 to ensure one can really “detect”significant changes in the process one is measuring1/24/03Measurement error 220

IsoplotProcedure: Use normal productionline parts to measure1. Measure part A and call “measurement 1”2. At a different time (12 - 14 hours later) measuresame part A call “measurement 2”.3. Keep data paired for measurement 1 and 2 onsame part4. Send part on through rest of process.5. Obtain a second part after part A and repeatthis first and second measurement6. Continue this first and second measurement onthe same part for at least 20 different parts fromthe normal manufacturing list over time.7. Plot second measurement Vs first on square(equal units) graphical format1/24/03Measurement error 221

IsoplotProcedure:8. From the plot calculate a “length” or normal process variation range callthis P or X as shown below.9. From the plot calculate a “width” or the measurement variation rangecall this M.10. Shainin claims a 6 or greater ratio of P/M is required to ensure that themeasurement system can discriminate1/24/03Measurement error 222

Gage Study Example: Using Excel file Gage R&R Study Macro1/24/03Measurement error 223

Gage Study Example: Using Excel file “Gage R&R Study” MacroInput CD data: five sites on a wafer; Measured 3 times(Trials)Repeatability and Done 3 times (Runs) Operator to OperatorReproducibilityR&R StudySTANDARD GAGE STUDYNumber of Runs 3Gage:SEM 05Number of Sites 5Part:wafer 0.18um linNumber of Trials 3Tolerance 0.12Enter data and Information in open cells*If Range Check displays "FLAG", check data0.2Date:Performed By:28-Sep-01John DoeIsoplotMeasurement Site on erageTrials(ΣB)2wafer Check*Part 4222220.18654 0.18758Measurement error 20.1950.190.180.170.170.1750.180.1850.1924

Gage Study Example: Using Excel file “Gage R&R Study” MacroANOVADFSSMSappraisers number of 2044E-06Total440.0009258887.8322E-06Parts (sites)appraisers*PartsF MS ap/MseProb F1.5492292350.182359224appraiser*Part Interaction is Not SignificantEnter Process Distribution Width in Sigma's (5.15 or 6.00). For One-Sided Spec, Enter 36.00SIGMAVARIATIONPERCENT OFTOTAL VARIATIONPERCENT OFTOLERANCERepeatability (EV - Equipment Var)0.002800.0167957.10%13.99%Reproducibility (AV - appraiser or Operator Var)0.000530.0031610.76%2.64%Repeatability & Reproducibility (R&R)0.002850.0170958.10%14.24%Part Variation (PV)0.003990.0239481.39%19.95%Total Process Variation (TV)0.004900.02941SOURCE OF VARIATIONappraiser * Equipment Interaction (IV)24.51%Note: Percentages will not add to 100%.R&R Criteria P/T 1/6 16.67%The result of this analysis:PASSFor measurement systems whose purpose is to analyze a process, general rules of thumb are:Acceptability Criteria for %R&R (% of Total Variation and % of Tolerance)9 Under 10% - acceptable system - Under 5% preferred9 10% to 30% - may be acceptable depending on importance of the application, cost of the system, cost of repair, etc9 Over 30% - considered not acceptable - every effort should be made to improve the system1/24/03Measurement error 225

Gage Study Example: Using Excel file “Gage R&R Study” MacroANOVADFSSMSappraisers number of 2044E-06Total440.0009258887.8322E-06Parts (sites)appraisers*PartsF MS ap/MseProb F1.5492292350.182359224appraiser*Part Interaction is Not SignificantA significant appraisers*Parts interaction means that appraistend to obtain different measurements from identical partsEnter Process Distribution Width in Sigma's (5.15 or 6.00). For One-Sided Spec, Enter 36.00The AIAG method uses 5.15, other customers may use 6.00PERCENT OFTOLERANCESIGMAVARIATIONPERCENT OFTOTAL VARIATIONRepeatability (EV - Equipment Var)0.002800.0167957.10%13.99%Reproducibility (AV - appraiser or Operator Var)0.000530.0031610.76%2.64%SOURCE OF VARIATIONIf Prob F is 0.05 or smaller, then appraisers*Parts interactionis significant; check plots to determine whyappraiser * Equipment Interaction (IV)5.15 standard deviations enclose the central 99% of anormal distributionIf %R&R of Tolerance is blank, enter a Tolerance above14.24%Repeatability & Reproducibility (R&R)0.002850.0170958.10%14.24%Part Variation (PV)0.003990.0239481.39%19.95%Total Process Variation (TV)0.004900.02941% R&R of Total Variation (RSS of EV AV)but see the quote from AIAG below24.51%Note: Percentages will not add to 100%.R&R Criteria P/T 1/6 16.67%The result of this analysis:PASSFor measurement systems whose purpose is to analyze a process, general rules of thumb are:Acceptability Criteria for %R&R (% of Total Variation and % of Tolerance)9 Under 10% - acceptable system - Under 5% preferred9 10% to 30% - may be acceptable depending on importance of the application, cost of the system, cost of repair, etc9 Over 30% - considered not acceptable - every effort should be made to improve the systemAIAG uses 10%, but within Motorola 5% is preferred(Note: For %R&R smaller is better)AIAG Automotive Industry Action Group1/24/03Measurement error 226

Sources of ErrorVariation (defined as sigma) in building a product will use a RSS approach tofind total variation: Example here is fro five assembly steps11/24/0323Measurement error 24527

Sources of ErrorError propagation model: Used to find total variation after product iscompletely builtThe formula for error propagationIf f F(x,y,z ) and you want σf and you haveσx, σy, σz , then use the following formula:2σf1/24/0322 F 2 F 2 F 2 σ y σ x σ z . x z y Measurement error 228

1/24/03 Measurement_error_2 26 Gage Study Example: Using Excel file “Gage R&R Study” Macro ANOVA DF SS MS F MS ap/Mse Prob F appraisers number of runs 2 2.40053E-05 1.20027E-05 Parts (sites) 4 0.000604259 0.000151065 appraisers*Parts 8 8.70102E-05 1.08763E-05 1.549229235 0.182359224 If Prob F is 0.05 or smaller, then appraisers*Parts interactio Gage(Error) 30 0.000210613 7.02044E-06 .

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