2Statistical Analysis; PWL Estimate Verify Production Process: Payment OverviewP 401 Test ResultsStatistical Analysis; PWL EstimateVerify Production Process: Payment
3Theory Assumptions Normal Distribution Tools: Average and Standard DeviationPercent Within Limits (PWL) Concept
4AssumptionsLimited # of test results Statistical Analysis Quality characteristics of large amount of materialTest result variabilityComponents:materialssampling-ERLPMtesting-ERLPMSame ProcessRandom sampling-Lot, SublotNormal Distribution
14Roundout Rules ERLPM-page 47 Example-last digit to be kept-nearest 10th4.614.624.644.65004.664.674.684.69Even Digit-sameOdd Digit-increase by 1This case becomes 4.6If it was it would become 4.8becomes 4.7
28Test for Outliers MAT Density 94.0 QL= 96.2-96.3 = -.0585 96.0 1.71 97.098.0x= 96.2Sn= 1.71QL= =1.71PL= <50%ASTM E 178, par. 4T1= (x-x1)/SnT1= = 1.2861.71
29Table 1-ASTM E 178N=4Upper 5% significance level 1.463Since 1.286<1.463 the 94.0 test value is not considered an outlier and is retained!
30Sample Problem-Outliers Air Voids2.0, 4.8, 4.9, 5.0X=4.2Sn=1.45QL= = ; PL= 1001.45QU= = ; PU= 69PWL= (100+69)-100=69ASTM E 178 par. 4Tn= (x-x1)/Sn = = 1.517Table 1, ASTM E 178, N=4, 5% significanceT= 1.463<1.517therefore 2.0 is the outlier and it is discarded
31Resampling 401-5.3 page 25 MAT Density ONLY (Appendix E-pg 4) Prior MAT Density- 96, 97, 99, 100PWL 824 new cores 96, 96, 97, 98AVG-all 8, 97.4Sn= 1.51QL= x-L = = .7337SnTable 1, N= 8PWL= 77