INSTRUCTIONS

GAGE LINEARITY & BIAS STUDY1. For this Template Select the gage first on which you want to do the study.2. Select the Quality Characteristic which this gage measures. 3.Take Five (5) Reference values for the test specimen you are going to measure.4.Plug these values in the spreadsheet marked as red under the "Reference Values" Heading.5. Take 10 repeated measurements on the Test Specimen by five different Appraisers for each Reference Value.6. Plug this data in the Red Shaded Region and Get the results.7. For Linearity - Look in the Absolute value of tm. Select t - statistics from T - Dist Table for n - 2 or 10 - 2 = 8 degrees of freedom at 97.5% Confidence Level i.e. at 0.975 or a = 0.05. This will be called tCritical. If tm < t Critical the Gage is OK and linear. If tm > tCritical the gage should be recalibrated after repair.8. For Linearity there is a Graphical Check also in the Template. If the Correlation Coefficient R2 is > 0.60 the gage is linear and OK.9. For Bias Study Similarly Plug in the reference values and the Tested Values in the red shaded region. Look for the value of tBias in the spreadsheet. 10. Look further for t - statistics from T - Dist Table for n - 2 = 10 - 2 = 8 Degrees of freedom at 97.5% Confidence Level or at a = 0.05. This value will be called tCritical.11. If tBias < tCritical we say Bias = 0 and the measurement device is OK. If tBias > tCritical we Conclude Bias is not zero and the measurement system should be repaired and recalibrated.

GAGE LINEARITY STUDYGAGE LINEARITY STUDY TEMPLATEREFRENCE VALUESREF. VALUEAVG. OF TRIAL READINGS1.21.2281.211.233ABCDESUMSQUARES(X-X)21.31.2751.21.211.31.251.246.238.440.00621.251.281SQUARES1.441.46411.691.56251.53767.69421.241.238S.NO.TRIALS VALUES AGAINST EACH REF. VALUEAVG. OF REF. VALUES = X1.2411.211.221.251.261.2521.211.231.261.281.2631.221.251.271.291.2441.231.241.291.31.2551.241.261.261.281.2361.251.211.271.291.2271.21.221.291.281.2481.241.231.281.291.2191.261.221.31.251.23101.221.251.281.291.25AVERAGE1.2281.2331.2751.2811.238RANGE0.060.050.050.050.05PRODUCT OF EACH BIAS VALUE & ITS REFERENCE VALUESQUARE OF BIAS VALUESS.NO.BIAS VALUES10.010.01-0.050.010.010.0120.0121-0.0650.01250.01240.00010.00010.00250.00010.000120.010.02-0.040.030.020.0120.0242-0.0520.03750.02480.00010.00040.00160.00090.000430.020.04-0.030.0400.0240.0484-0.0390.0500.00040.00160.00090.0016040.030.03-0.010.050.010.0360.0363-0.0130.06250.01240.00090.00090.00010.00250.000150.040.05-0.040.03-0.010.0480.0605-0.0520.0375-0.01240.00160.00250.00160.00090.000160.050-0.030.04-0.020.060-0.0390.05-0.02480.002500.00090.00160.0004700.01-0.010.03000.0121-0.0130.0375000.00010.00010.0009080.040.02-0.020.04-0.030.0480.0242-0.0260.05-0.03720.00160.00040.00040.00160.000990.060.0100-0.01GRAND MEAN0.0720.012100-0.01240.00360.0001000.0001100.020.04-0.020.040.010.0240.0484-0.0260.050.01240.00040.00160.00040.00160.0001AVERAGE0.0280.023-0.0250.031-0.0020.011SUM0.3360.2783-0.3250.3875-0.0248SUM0.0413SUM0.280.23-0.250.31-0.02SXY0.652FUNCTIONAL VARIABLES0.55(SXSY)/(10)0.341Y = (m)X + b Where m = slope. If Value of tm is less than or equal to t value at n - 2 degrees of freedom and a = 0.05 we accept the null Hypothesis that Linearity = 0 and our Measurement system is OK and If tm > t value from T - Dist table at n - 2 degrees of freedom and a = 0.05 we reject the Null Hypothesis that Linearity = 0 and conclude that our Measurement System is not OK and we must recalibrate it after repair. Here n = 10 Therefore n - 2 = 8 Degrees of Freedomb-0.0891610306SX27.6942m0.0807750247(S(X)2)/(10)3.844tm0.0926832789SLOPE0.0807750247s0.068623293SY20.0413SY0.55From T - Dist Table tCritical at (n-2) = 8 Degrees of freedom and a = 0.05 is 2.306. Therefore tm < tCritical we accept the Hypothesis that Linearity = 0 which implies that The Measurement System for measuring BULK of Paper is OK

GAGE LINEARITY STUDY00000

GAGE BIAS STUDY GAGE BIAS STUDY TEMPLATEREFRENCE VALUESABCDESUMSQUARES(X-X)21.21.211.31.251.246.238.440.0062SQUARES1.441.46411.691.56251.53767.6942S.NO.TRIALS VALUES AGAINST EACH REF. VALUEAVG. OF REF. VALUES = X1.2411.211.221.251.261.2521.211.231.261.281.26(X)21.537631.221.251.271.291.2441.231.241.291.31.2551.241.261.261.281.2361.251.211.271.291.2271.21.221.291.281.2481.241.231.281.291.2191.261.221.31.251.23101.221.251.281.291.25AVERAGE1.2281.2331.2751.2811.238RANGE0.060.050.050.050.05PRODUCT OF EACH BIAS VALUE & ITS REFERENCE VALUESQUARE OF BIAS VALUESS.NO.BIAS VALUES10.010.01-0.050.010.010.0120.0121-0.0650.01250.01240.00010.00010.00250.00010.000120.010.02-0.040.030.020.0120.0242-0.0520.03750.02480.00010.00040.00160.00090.000430.020.04-0.030.0400.0240.0484-0.0390.0500.00040.00160.00090.0016040.030.03-0.010.050.010.0360.0363-0.0130.06250.01240.00090.00090.00010.00250.000150.040.05-0.040.03-0.010.0480.0605-0.0520.0375-0.01240.00160.00250.00160.00090.000160.050-0.030.04-0.020.060-0.0390.05-0.02480.002500.00090.00160.0004700.01-0.010.03000.0121-0.0130.0375000.00010.00010.0009080.040.02-0.020.04-0.030.0480.0242-0.0260.05-0.03720.00160.00040.00040.00160.000990.060.0100-0.01GRAND MEAN0.0720.012100-0.01240.00360.0001000.0001100.020.04-0.020.040.010.0240.0484-0.0260.050.01240.00040.00160.00040.00160.0001AVERAGE0.0280.023-0.0250.031-0.0020.011SUM0.3360.2783-0.3250.3875-0.0248SUM0.0413SUM0.280.23-0.250.31-0.02SXY0.652FUNCTIONAL VARIABLES0.55(SXSY)/(10)0.341Y = (m)X + b Where m = slope. If Value of tm is less than or equal to t value at n - 2 degrees of freedom and a = 0.05 we accept the null Hypothesis that Linearity = 0 and our Measurement system is OK and If tm > t value from T - Dist table at n - 2 degrees of freedom and a = 0.05 we reject the Null Hypothesis that Linearity = 0 and conclude that our Measurement System is not OK and we must recalibrate it after repair. Here n = 10 Therefore n - 2 = 8 Degrees of Freedomb-0.0891610306SX27.6942m0.0807750247(S(X)2)/(10)3.844tm0.0926832789SLOPE0.0807750247s0.068623293SY20.0413tBias0.0824878802SY0.55From T - Dist Table tCritical at (n-2) = 8 Degrees of freedom and a = 0.05 is 2.306. Therefore tBias < tCritical we accept the Hypothesis that bias = 0 which implies that The Measurement System for measuring BULK of Paper is OK

THE LINE OF BEST FIT HERE HAS CORRELATION COEFFICIENT = 0.6612OR 66.12% WHICH IS GREATER THAN0.60 OR 60%. THEREFORE GRAPHICALLYALSO WE CAN CONCLUDE THAT OURMEASUREMENT SYSTEM FOR MEASURING BULK OF PAPER IS OK!

EXAMPLE LINEARITYGAGE LINEARITY STUDY TEMPLATEREFRENCE VALUESREF. VALUEAVG. OF TRIAL READINGS5757.4857.557.15ABCDESUMSQUARES(X-X)25857.135757.55858.559290841002.558.556.98SQUARES32493306.2533643422.25348116822.55957.08S.NO.TRIALS VALUES AGAINST EACH REF. VALUEAVG. OF REF. VALUES = X58157.457.556.456.657.4257.357.157.257.657.6357.456.656.757.458457.556.457.256.956.8558.757.157.556.756.6657.257.357.157.156.3757.957.657.45757.3856.458.257.756.956.3957.55757.156.556.51057.556.75757.158AVERAGE57.4857.1557.1356.9857.08RANGE2.31.81.31.11.7PRODUCT OF EACH BIAS VALUE & ITS REFERENCE VALUESQUARE OF BIAS VALUESS.NO.BIAS VALUES10.40-1.6-1.9-1.622.80-92.8-111.15-94.40.1602.563.612.5620.3-0.4-0.8-0.9-1.417.1-23-46.4-52.65-82.60.090.160.640.811.9630.4-0.9-1.3-1.1-122.8-51.75-75.4-64.35-590.160.811.691.21140.5-1.1-0.8-1.6-2.228.5-63.25-46.4-93.6-129.80.251.210.642.564.8451.7-0.4-0.5-1.8-2.496.9-23-29-105.3-141.62.890.160.253.245.7660.2-0.2-0.9-1.4-2.711.4-11.5-52.2-81.9-159.30.040.040.811.967.2970.90.1-0.6-1.5-1.751.35.75-34.8-87.75-100.30.810.010.362.252.898-0.60.7-0.3-1.6-2.7-34.240.25-17.4-93.6-159.30.360.490.092.567.2990.5-0.5-0.9-2-2.5GRAND MEAN28.5-28.75-52.2-117-147.50.250.250.8146.25100.5-0.8-1-1.4-128.5-46-58-81.9-590.250.6411.961AVERAGE0.48-0.35-0.87-1.52-1.92-0.836SUM273.6-201.25-504.6-889.2-1132.8SUM82.88SUM4.8-3.5-8.7-15.2-19.2SXY-2454.25FUNCTIONAL VARIABLES-41.8(SXSY)/(10)-1212.2Y = (m)X + b Where m = slope. If Value of tm is less than or equal to t value at n - 2 degrees of freedom and a = 0.05 we accept the null Hypothesis that Linearity = 0 and our Measurement system is OK and If tm > t value from T - Dist table at n - 2 degrees of freedom and a = 0.05 we reject the Null Hypothesis that Linearity = 0 and conclude that our Measurement System is not OK and we must recalibrate it after repair. Here n = 10 Therefore n - 2 = 8 Degrees of Freedomb7.7273164933SX216822.5m-0.1476433878(S(X)2)/(10)8410tm-0.100079337SLOPE-0.1476433878s2.3325963237SY282.88ABS (tm)0.100079337SY-41.8From T - Dist Table tCritical at (n-2) = 8 Degrees of freedom and a = 0.05 is 2.306. Therefore tm < tCritical we accept the Hypothesis that Linearity = 0 which implies that The Measurement System for measuring GSM of Paper is OK

EXAMPLE LINEARITY57.4857.1557.1356.9857.08

EXAMPLE BIASGAGE BIAS STUDY TEMPLATEREFRENCE VALUESABCDESUMSQUARES(X-X)25757.55858.559290841002.5SQUARES32493306.2533643422.25348116822.5S.NO.TRIALS VALUES AGAINST EACH REF. VALUEAVG. OF REF. VALUES = X58157.457.556.456.657.4257.357.157.257.657.6(X)23364357.456.656.757.458457.556.457.256.956.8558.757.157.556.756.6657.257.357.157.156.3757.957.657.45757.3856.458.257.756.956.3957.55757.156.556.51057.556.75757.158AVERAGE57.4857.1557.1356.9857.08RANGE2.31.81.31.11.7PRODUCT OF EACH BIAS VALUE & ITS REFERENCE VALUESQUARE OF BIAS VALUESS.NO.BIAS VALUES10.40-1.6-1.9-1.622.80-92.8-111.15-94.40.1602.563.612.5620.3-0.4-0.8-0.9-1.417.1-23-46.4-52.65-82.60.090.160.640.811.9630.4-0.9-1.3-1.1-122.8-51.75-75.4-64.35-590.160.811.691.21140.5-1.1-0.8-1.6-2.228.5-63.25-46.4-93.6-129.80.251.210.642.564.8451.7-0.4-0.5-1.8-2.496.9-23-29-105.3-141.62.890.160.253.245.7660.2-0.2-0.9-1.4-2.711.4-11.5-52.2-81.9-159.30.040.040.811.967.2970.90.1-0.6-1.5-1.751.35.75-34.8-87.75-100.30.810.010.362.252.898-0.60.7-0.3-1.6-2.7-34.240.25-17.4-93.6-159.30.360.490.092.567.2990.5-0.5-0.9-2-2.5GRAND MEAN28.5-28.75-52.2-117-147.50.250.250.8146.25100.5-0.8-1-1.4-128.5-46-58-81.9-590.250.6411.961AVERAGE0.48-0.35-0.87-1.52-1.92-0.836SUM273.6-201.25-504.6-889.2-1132.8SUM82.88SUM4.8-3.5-8.7-15.2-19.2SXY-2454.25FUNCTIONAL VARIABLES-41.8(SXSY)/(10)-1212.2Y = (m)X + b Where m = slope. If Value of tm is less than or equal to t value at n - 2 degrees of freedom and a = 0.05 we accept the null Hypothesis that Linearity = 0 and our Measurement system is OK and If tm > t value from T - Dist table at n - 2 degrees of freedom and a = 0.05 we reject the Null Hypothesis that Linearity = 0 and conclude that our Measurement System is not OK and we must recalibrate it after repair. Here n = 10 Therefore n - 2 = 8 Degrees of Freedomb7.7273164933SX216822.5m-0.1476433878(S(X)2)/(10)8410tm-0.100079337SLOPE-0.1476433878s2.3325963237SY282.88tBias0.0903056634SY-41.8From T - Dist Table tCritical at (n-2) = 8 Degrees of freedom and a = 0.05 is 2.306. Therefore tBias < tCritical we accept the Hypothesis that bias = 0 which implies that The Measurement System for measuring GSM of Paper is OK

THE LINE OF BEST FIT HERE HAS CORRELATION COEFFICIENT = 0.662OR 66.2% WHICH IS GREATER THAN0.60 OR 60%. THEREFORE GRAPHICALLYALSO WE CAN CONCLUDE THAT OURMEASUREMENT SYSTEM FOR MEASURING GSM OF PAPER IS OK!

T-Dista = .051-sideda = .052-sided1 - .05 =.951-sided2-sidedAlpha Risk0.6000.7000.8000.9000.9500.9750.9900.995DF = n-110.3250.7271.3763.0786.31412.70631.82163.65720.2890.6171.0611.8862.9204.3036.9659.92530.2770.5840.9781.6382.3533.1824.5415.84140.2710.5690.9411.5332.1322.7763.7474.60450.2670.5590.9201.4762.0152.5713.3654.03260.2650.5530.9061.4401.9432.4473.1433.70770.2630.5490.8961.4151.8952.3652.9983.49980.2620.5460.8891.3971.8602.3062.8963.35590.2610.5430.8831.3831.8332.2622.8213.250100.2600.5420.8791.3721.8122.2282.7643.169110.2600.5400.8761.3631.7962.2012.7183.106120.2590.5390.8731.3561.7822.1792.6813.055130.2590.5380.8701.3501.7712.1602.6503.012140.2580.5370.8681.3451.7612.1452.6242.977150.2580.5360.8661.3411.7532.1312.6022.947160.2580.5350.8651.3371.7462.1202.5832.921170.2570.5340.8631.3331.7402.1102.5672.898180.2570.5340.8621.3301.7342.1012.5522.878190.2570.5330.8611.3281.7292.0932.5392.861200.2570.5330.8601.3251.7252.0862.5282.845210.2570.5320.8591.3231.7212.0802.5182.831220.2560.5320.8581.3211.7172.0742.5082.819230.2560.5320.8581.3191.7142.0692.5002.807240.2560.5310.8571.3181.7112.0642.4922.797250.2560.5310.8561.3161.7082.0602.4852.787260.2560.5310.8561.3151.7062.0562.4792.779270.2560.5310.8551.3141.7032.0522.4732.771280.2560.5300.8551.3131.7012.0482.4672.763290.2560.5300.8541.3111.6992.0452.4622.756300.2560.5300.8541.3101.6972.0422.4572.750400.2550.5290.8511.3031.6842.0212.4232.704600.2540.5270.8481.2961.6712.0002.3902.6601200.2540.5260.8451.2891.6581.9802.3582.6170.2530.5240.8421.2821.6451.9602.3262.576

&C&"Arial,Bold Italic"&14T-Distribution