BSI - Measurement System Analysis (MSA)

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Measurement System Analysis

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<ul><li> 1. Copyright 2013 BSI. All rights reserved.Measurement System AnalysisMeasurement System Analysis</li></ul><p> 2. Copyright 2013 BSI. All rights reserved. 3. Copyright 2013 BSI. All rights reserved. 3 (Measurement System Discrimination) , Measurement System AnalysisVariable Measurement System StudyStabilityBias Control ChartLinearityRepeatability and ReproducibilityRange MethodAverage and Range MethodAttribute Measurement System Study 4. Copyright 2013 BSI. All rights reserved. 47.6 (Control of monitoring and measuring equipment) ,, (basis used) ( 4.2.4) 5. Copyright 2013 BSI. All rights reserved. 5 ( 4.2.4) 6. Copyright 2013 BSI. All rights reserved. 6 7.6.1 (intended application) configuration management 7. Copyright 2013 BSI. All rights reserved. 7 MSA Total2Product2Measurement System2==== ++++ 8. Copyright 2013 BSI. All rights reserved. 8Actual process variationProduction gage variation Observed process variationObserved process variation 9. Copyright 2013 BSI. All rights reserved. 9? 10. Copyright 2013 BSI. All rights reserved. 10MeasurementSystemDiscrimination 11. Copyright 2013 BSI. All rights reserved. 11 (Categories) Measurement System Discrimination = Resolution 12. Copyright 2013 BSI. All rights reserved. 12Resolution = 1 cmonly 0 cmor 1 cm1 category1cm0ABC 13. Copyright 2013 BSI. All rights reserved. 131cm0ABCDResolution = 0.5 cm0 cm / 0.5 cm / 1 cm2 categories0.5 14. Copyright 2013 BSI. All rights reserved. 141cm0ABCDResolution = 0.1 cm00.10.20.3...0.91.0 cm10 categories0.5 15. Copyright 2013 BSI. All rights reserved. 151cm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9A1A2A3Resolution = 0.1 cmA1 = 0.12A2 = 0.15A3 = 0.190.12 , 0.15 , 0.192 0.1 0.2 cm 16. Copyright 2013 BSI. All rights reserved. 16Discrimination Unacceptable for analysis.if. it cannot detect the variation of the processDiscrimination Unacceptable for control .ifit cannot detect the special cause variation 17. Copyright 2013 BSI. All rights reserved. 17XPROCESS VARIATION= 60 1Situation Analysis ControlRes. = 1 &gt; 61 data category6 &lt; Res. &lt; Tol NG OK Spec 18. Copyright 2013 BSI. All rights reserved. 18XPROCESS VARIATION= 6 0 0.5 1Situation Analysis ControlRes. = 0.1 &lt; 655 or morecategoriesAcceptable Variable Controlchart 19. Copyright 2013 BSI. All rights reserved. 19XPROCESS VARIATION= 6 0 2Situation Analysis ControlRes. &gt; Tol Unacceptable Unacceptable 20. Copyright 2013 BSI. All rights reserved. 20RecommendationResolution = 1 Process Variation10= 1 610XPROCESS VARIATION= 6 TOLERANCE110 6 resolution resolution (process variation) 21. Copyright 2013 BSI. All rights reserved. 21Traditional RuleResolution = 1 Tolerance10ButThe less 6 the moreunacceptable resolutionXPROCESS VARIATION= 6 TOLERANCE110 Tol 22. Copyright 2013 BSI. All rights reserved. 22 X bar- R chart Resolution Range chart. Range chart 1, 2, 3 Control limits, Resolution Range chart 4 Controllimits 1 4 0 Resolution Resolution X bar-R Chart 23. Copyright 2013 BSI. All rights reserved. 23These control charts derived from the same samples0.1470.1450.1430.1410.1390.1370.135X-bar Chart for Resolution 0.001UCLx LCLx X-bar-bar X bar0.1470.1450.1430.1410.1390.1370.135X-bar Chart for Resolution 0.01UCLx LCLx X-bar-bar X bar 0.0250.020.0150.010.0050R-Chart for Resolution 0.001UCLr LCLr R-bar R 0.0250.020.0150.010.0050R-Chart for Resolution 0.01UCLr LCLr R-bar R Adequate resolution Inadequate resolutionless than4 possiblevalueswithincontrollimitmore than1/4 of therangesare zero 24. Copyright 2013 BSI. All rights reserved. 24 (Accuracy) (Precision) 25. Copyright 2013 BSI. All rights reserved. 25 (Accuracy) (master) (true) , , (e.g., NIST)MasterValueMeanBias 26. Copyright 2013 BSI. All rights reserved. 26 (Total variation) (Repeatabilityand Reproducibility) (Precision) MS rpt rpd2 2 2= + MS rpt rpd2 2 2= + 27. Copyright 2013 BSI. All rights reserved. 27 ( inherent variability) Same operatorSame set-upSame unitsSame environmental conditionsShort-term: r p t 3? 28. Copyright 2013 BSI. All rights reserved. 28 (Repeatability) /(test - retest error); (short-term variation)MasterValueMeanGoodRepeatabilityPoorRepeatability 29. Copyright 2013 BSI. All rights reserved. 29 ( differentconditions)Different operatorsDifferent set-upsDifferent test unitsDifferent environmental conditionsLong-term: rpd3? 30. Copyright 2013 BSI. All rights reserved. 30 (Reproducibility)MasterValueGoodReproducibilityOperator 1PoorReproducibilityOperator 2 Operator 3Operator 1Operator 2Operator 3 31. Copyright 2013 BSI. All rights reserved. 31 (true) 5.0 1 :3.8, 4.4, 4.2, 4.0 2 :6.5, 4.0, 3.2, 6.3 ? 2 ( )? 1 ()? ? (correction) vs. 32. Copyright 2013 BSI. All rights reserved. 32MSA Selection ProcedureDataTypeVariable data Attribute dataFocusAccuracy PrecisionGauge LinearityStability Gauge R&amp;R StudyAttributeAgreement Analysis Bias Study 33. Copyright 2013 BSI. All rights reserved. 33 34. Copyright 2013 BSI. All rights reserved. 34 Stability 35. Copyright 2013 BSI. All rights reserved. 35Time 1Time 1Time 2Time 3Time 2 (Stability)MasterValueMasterValueGoodStabilityPoorStabilityTime 3 36. Copyright 2013 BSI. All rights reserved. 36 StabilityStability ()Time 1Time 2X1X2 37. Copyright 2013 BSI. All rights reserved. 37 Stability 1 2 6.01 Stability 38. Copyright 2013 BSI. All rights reserved. 38 3 3-5 25 (subgroup) 4 Xbar R Xbar-R chart (Control Limit) Stability 39. Copyright 2013 BSI. All rights reserved. 39 - Rk = kRRRR k+++=...21kxxxx k+++=...21RDUCLR 4= RDLCLR 3=RAxUCLx 2+= RAxLCLx 2=xnxxxx n+++=...21n = minmax xxR = 40. Copyright 2013 BSI. All rights reserved. 40 D4 , D3 A2n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31For sample size below 7, the LCLR would be negative number,In this case there is no lower control limit - Rx 41. Copyright 2013 BSI. All rights reserved. 41 5 Stability R chart Repeatability (Unstable repeatability)) Xbar chart (Unstability) Stability 42. Copyright 2013 BSI. All rights reserved. 42 UCLLCLCL Rx , 43. Copyright 2013 BSI. All rights reserved. 43 UCLLCLCL1) special cause x 44. Copyright 2013 BSI. All rights reserved. 442) (Trend) 7 UCLCLLCLRx , 45. Copyright 2013 BSI. All rights reserved. 45UCLLCLCL3) () 7 process shift Rx , 46. Copyright 2013 BSI. All rights reserved. 46 UCLLCLCLAABBCC4) A-A 47. Copyright 2013 BSI. All rights reserved. 47UCLLCLCLAABBCC5) B-C 48. Copyright 2013 BSI. All rights reserved. 486) (Cycle) UCLLCLCL process parameter 49. Copyright 2013 BSI. All rights reserved. 49Xbar Chart5.45.55.65.75.85.966.16.26.36.41 3 5 7 9 11 13 15 17 19XbarUCL=6.297CL=6.021LCL=5.746RChart00.20.40.60.811.2RUCL=1.010CL=0.4779LCL=0 50. Copyright 2013 BSI. All rights reserved. 50 5 R chart Xbar chart (Stability) (Stability) bias control chart R chart Stability 51. Copyright 2013 BSI. All rights reserved. 51 52. Copyright 2013 BSI. All rights reserved. 52 (Bias) (Referencevalue) (Observedaverage measurement) BIAS 53. Copyright 2013 BSI. All rights reserved. 53Bias bias = 0* BIAS 54. Copyright 2013 BSI. All rights reserved. 54 (BIAS) (Master Value): Operator bias - Instrument bias - MasterValueMeanInstrument 1 Instrument 2MeanInstrument 2 BiasInstrument 1 Bias 55. Copyright 2013 BSI. All rights reserved. 55 bias 2 1. bias 2. bias control chart R chart 30 T-Test BIAS0010=biasHbiasH 56. Copyright 2013 BSI. All rights reserved. 56 1 1 1 6.000 mm. Bias () 2 15 3 bias referencexbias ii =Reference Value ( g ) = 6.000BiasSample READING1 5.80 -0.202 5.70 -0.303 5.90 -0.104 5.90 -0.105 6.00 0.006 6.10 0.107 6.00 0.008 6.10 0.109 6.40 0.4010 6.30 0.3011 6.00 0.0012 6.10 0.1013 6.20 0.2014 5.60 -0.4015 6.00 0.00Mean 6.006667 0.007Std. Dev. 0.2120198 0.2120Max 6.400 0.400Min 5.600 -0.400Range 0.800 0.800 57. Copyright 2013 BSI. All rights reserved. 57 4Plot bias 0123456789-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 1E-16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Bias () 58. Copyright 2013 BSI. All rights reserved. 58nbiasbiasavgnii== 1_ 5 bias 6 repeatability1)( 21===nxxniirityrepeatabil Bias () 59. Copyright 2013 BSI. All rights reserved. 59[ ] [ ]TVTVEVEV ityrepeatabil /100/100 == 7 repeatabilityTV 6 8 t biasbbiasrbbiasaveragetstatistictn__ === Bias () 60. Copyright 2013 BSI. All rights reserved. 60 9 Bias pvalue pvalue 0 bias t)]([)]([21,21, +vbvb tBiaszerotBias1= n21,vtbiast 1 Bias () 61. Copyright 2013 BSI. All rights reserved. 61 1 1 1 6.000 mm. 15 Bias (Control Chart) 2 stability g (subgroup) 20 subgroup = mReference Value ( g ) = 6.000BiasSample READING1 5.80 -0.202 5.70 -0.303 5.90 -0.104 5.90 -0.105 6.00 0.006 6.10 0.107 6.00 0.008 6.10 0.109 6.40 0.4010 6.30 0.3011 6.00 0.0012 6.10 0.1013 6.20 0.2014 5.60 -0.4015 6.00 0.00Mean 6.006667 0.007Std. Dev. 0.2120198 0.2120Max 6.400 0.400Min 5.600 -0.400Range 0.800 0.800 62. Copyright 2013 BSI. All rights reserved. 62 3 Control Chart Stable, m=1 0123456789-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Bias (Control Chart) 4 m 2 Plot bias 63. Copyright 2013 BSI. All rights reserved. 63 5 Control Chart 6 repeatability*2dRrityrepeatabil == xreferencexbias = 7 repeatability standard deviation Average Range subgroup=(m) subgroup=(g) ( Appendix C)*2d Bias (Control Chart) 64. Copyright 2013 BSI. All rights reserved. 64[ ] [ ]TVTVEVEV ityrepeatabil /100/100 == 8 repeatabilityTV 6 9 t biasbbiasrbbiaststatistictgm===_ Bias (Control Chart) 65. Copyright 2013 BSI. All rights reserved. 65 9 Bias 0 bias ( Appendix C) t)]([)]([21,21, +vbvb tBiaszerotBias21,vt Bias (Control Chart) 66. Copyright 2013 BSI. All rights reserved. 66vd*2Appendix C 67. Copyright 2013 BSI. All rights reserved. 67 bias ( Master (Calibration) BIAS 68. Copyright 2013 BSI. All rights reserved. 68 69. Copyright 2013 BSI. All rights reserved. 69 (Operating Range) Linearity 70. Copyright 2013 BSI. All rights reserved. 70 (Linearity) ?AccuracyAccuracyAccuracyAccuracyGage 1:Linearity is an issue hereMeasurement UnitsMeasurement UnitsMeasurement UnitsMeasurement Units0AccuracyAccuracyAccuracyAccuracyGage 2:Linearity is not an issue here0Measurement UnitsMeasurement UnitsMeasurement UnitsMeasurement Units 71. Copyright 2013 BSI. All rights reserved. 71 1 5 (Operating Range) (Reference value) 2 reference value Linearity 72. Copyright 2013 BSI. All rights reserved. 72 3 5 10 5.00 mm. 25.00 mm. 5.10, 10.30, 15.00, 20.20, 25.00 mm. Linearity 73. Copyright 2013 BSI. All rights reserved. 73PART 1 2 3 4 5REFERENCEVALUE5.10 10.30 15.00 20.20 25.00T 1 5.10 10.30 14.99 20.20 25.002 5.10 10.30 15.00 20.19 25.00R 3 5.10 11.00 12.00 20.20 24.994 5.09 10.29 14.99 20.20 25.00I 5 5.10 11.00 15.00 20.18 24.996 5.10 10.30 14.99 20.20 25.00A 7 5.10 10.30 12.00 20.20 25.008 5.09 11.00 15.00 20.20 25.00L 9 5.10 10.29 15.00 20.19 25.0010 5.10 10.30 12.00 20.00 24.99S 11 5.10 10.29 15.00 20.20 25.0012 5.10 10.30 15.00 20.19 25.00PART Avg. 5.0983 10.4725 14.2475 20.1792 24.9975 74. Copyright 2013 BSI. All rights reserved. 74 3 ; Linearityreferencexbias jiji = ,,tmeasuremenofnumber;AveragePart == nnxmbiasbiasmjjii==1, 75. Copyright 2013 BSI. All rights reserved. 75PART 1 2 3 4 5REFERENCEVALUE5.10 10.30 15.00 20.20 25.001 0.00 0.00 -0.01 0.00 0.002 0.00 0.00 0.00 -0.01 0.00B 3 0.00 0.70 -3.00 0.00 -0.014 -0.01 -0.01 -0.01 0.00 0.00I 5 0.00 0.70 0.00 -0.02 -0.016 0.00 0.00 -0.01 0.00 0.00A 7 0.00 0.00 -3.00 0.00 0.008 -0.01 0.70 0.00 0.00 0.00S 9 0.00 -0.01 0.00 -0.01 0.0010 0.00 0.00 -3.00 -0.20 -0.0111 0.00 -0.01 0.00 0.00 0.0012 0.00 0.00 0.00 -0.01 0.00BIAS Avg. -0.0017 0.1725 -0.7525 -0.0208 -0.0025 76. Copyright 2013 BSI. All rights reserved. 76 Linearity 4 bias (Reference Value)-1.00-0.80-0.60-0.40-0.200.000.200.400.600.801.002.00 7.00 12.00 17.00 22.00 27.00BiasReference ValueLinearity Plot Upper boundBest fitLower boundbias=0BIAS Avg. 77. Copyright 2013 BSI. All rights reserved. 77 5 Bias Reference Value linearity Linearity 78. Copyright 2013 BSI. All rights reserved. 780.00005.000010.000015.000020.000025.000030.00000.00 5.00 10.00 15.00 20.00 25.00 30.00ObservedAverageValueReference ValueLinearity (Varying Linear Bias)PART Avg.No BIAS 79. Copyright 2013 BSI. All rights reserved. 79 6 Linearity Linearity( )slopexgmxyxgmxya ==22 11intercept== xayb22= gmyxaybys iiii( )( ) ++sxxxxgmtaxblowerigm2122021,201: ( )( ) +++sxxxxgmtaxbupperigm2122021,201: 80. Copyright 2013 BSI. All rights reserved. 80 6 Linearity Linearitybaxy ii +=averagebiasyi _=valuerederencexi _=( )1317.01122===slopexgmxyxgmxya0.7367intercept=== xayb 81. Copyright 2013 BSI. All rights reserved. 81 6 repeatabilitySityrepeatabil =[ ] [ ]TVTVEVEV ityrepeatabil /100/100 == 7 repeatabilityTV 6 Linearity 82. Copyright 2013 BSI. All rights reserved. 82[ ] [ ]TVTVEVEV ityrepeatabil /100/100 == 7 repeatabilityTV 6 8Plot bias Bias () 83. Copyright 2013 BSI. All rights reserved. 83 9, 0:0 =aH( )21,22=gmitxxSat0:0 =bH( )21,2221+=gmitSxxxgmbt Linearity 84. Copyright 2013 BSI. All rights reserved. 84 10 (Acceptance criteria) Linearity (Error) ( 0) Linearity 85. Copyright 2013 BSI. All rights reserved. 85 10 (Acceptance criteria) LinearityStatistic Testing ResultTEST for slope TEST for interceptH0: a = 0 H0: b = 0H1: a 0 H1: b 0ta =0.13061303 tb = 0.1699136[ X ]ta tgm-2,1-/2[ X ]tb tgm-2,1-/2Accept H0, Reject H1 Accept H0, Reject H1[ ]ta &gt; tgm-2,1-/2[ ]tb &gt; tgm-2,1-/2Reject H0, Aacept H1 Reject H0, Aacept H1 86. Copyright 2013 BSI. All rights reserved. 861. 2. 3. 4. 87. Copyright 2013 BSI. All rights reserved. 87 88. Copyright 2013 BSI. All rights reserved. 88 2 (Repeatability) (Reproducibility) (Precision) 89. Copyright 2013 BSI. All rights reserved. 89 (Precision)TS-APQP-189Accurate () Not AccuratePrecise()Not Precise 90. Copyright 2013 BSI. All rights reserved. 90 (Repeatability) (Repeatability) (Shot-Term Measurement) (Repeatability) 91. Copyright 2013 BSI. All rights reserved. 91 (Repeatability)Good RepeatabilityReference ValuePoor RepeatabilityReference Value 92. Copyright 2013 BSI. All rights reserved. 92 (Reproducibility) (Long-Term Measurement) (Reproducibility) 93. Copyright 2013 BSI. All rights reserved. 93 (Reproducibility)Appraiser AReference ValueAppraiser BAppraiser C Appraiser AAppraiser BAppraiser CReference ValueGood Reproducibility Poor Reproducibility 94. Copyright 2013 BSI. All rights reserved. 94 Repeatability Reproducibility Gage Repeatabilityand Reproducibility (GRR) Gage R&amp;R 3 (Range Method) (...</p>