Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis;...
-
Upload
kallie-shacklett -
Category
Documents
-
view
217 -
download
2
Transcript of Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis;...
![Page 1: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/1.jpg)
Statistical AnalysisStatistical Analysis
Carl SteinhauerCarl Steinhauer
ConsultantConsultant
![Page 2: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/2.jpg)
OverviewOverview
P 401 Test ResultsP 401 Test Results
Statistical Analysis; PWL EstimateStatistical Analysis; PWL Estimate
Verify Production Process: PaymentVerify Production Process: Payment
![Page 3: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/3.jpg)
TheoryTheory
1.1. AssumptionsAssumptions
2.2. Normal DistributionNormal Distribution
3.3. Tools: Average and Standard Tools: Average and Standard DeviationDeviation
4.4. Percent Within Limits Percent Within Limits (PWL) Concept(PWL) Concept
![Page 4: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/4.jpg)
AssumptionsAssumptions
1.1. Limited # of test resultsLimited # of test results Statistical Analysis Statistical Analysis Quality characteristics of large amount of materialQuality characteristics of large amount of material
2.2. Test result variabilityTest result variability
Components:Components:
materialsmaterials
sampling-ERLPMsampling-ERLPM
testing-ERLPMtesting-ERLPM
3.3. Same ProcessSame Process
4.4. Random sampling-Lot, SublotRandom sampling-Lot, Sublot
5.5. Normal DistributionNormal Distribution
![Page 5: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/5.jpg)
Specific ProceduresSpecific Procedures
1.1. Sublots, Lots, Partial LotsSublots, Lots, Partial Lots
2.2. CalculationsCalculations
3.3. RetestingRetesting
4.4. OutliersOutliers
![Page 6: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/6.jpg)
AnalysisAnalysis
% Taller than 5’-5”% Taller than 5’-5”
% between 5’-5” and 6’-5”% between 5’-5” and 6’-5”
Average HeightAverage Height
Limit # of samplesLimit # of samples
Statistical AnalysisStatistical Analysis
Estimate average Estimate average and % within limits and % within limits
Population
0
10
20
30
40
50
60
70
80
4-7 4-9 5-1 5-3 5-5 5-7 5-9 5-11
6-1 6-3 6-5 6-7 6-9 6-11
Organize Date
Fre
qu
en
cy
![Page 7: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/7.jpg)
Figure 1
0
5
10
15
20
255.
45
5.55
5.65
5.75
5.85
5.95
6.05
6.15
6.25
6.35
6.45
6.55
Asphalt Content %
Fre
qu
ency n=100
96 tests96 tests
![Page 8: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/8.jpg)
0
10
20
30
40
50
60
2400
2375
2350
2325
2300
2275
2250
2225
2200
2175
2150
2125
2100
2075
2050
2025
2000
Marshall Stability
Freq
uenc
y
![Page 9: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/9.jpg)
x+/- 1Sn=68%x+/- 1Sn=68%
x+/-2Sn+95%x+/-2Sn+95%
x+/-3Sn+99.7%x+/-3Sn+99.7%
xx
![Page 10: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/10.jpg)
PWL Concept
LL=spec lower tolerance limitL=spec lower tolerance limit
eg. Mat density 96.3 for P401eg. Mat density 96.3 for P401
PWL-% of PWL-% of test result test result exceeding Lexceeding L
![Page 11: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/11.jpg)
PWL Calculation ProceduresPWL Calculation ProceduresERLPM-page 47ERLPM-page 47
Section 110-AC 1505370-10ASection 110-AC 1505370-10A
Method for Computing PWL and ExamplesMethod for Computing PWL and Examples
Section 110-02Section 110-02
Spec. P401 Table 5-L and U Spec. Limits (page 24)Spec. P401 Table 5-L and U Spec. Limits (page 24)
![Page 12: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/12.jpg)
GivenGiven
xx11=2=2
xx22=4=4
xx33=6=6
xx44=8=8
X = X = 2+4+6+82+4+6+8 = 5 = 5
44
![Page 13: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/13.jpg)
X=5X=5
dd11=2-5=-3=2-5=-3 dd11²=9²=9
dd22=4-5=-1=4-5=-1 dd22²=1²=1
dd33=6-5=1=6-5=1 dd33²=1²=1
dd44=8-5=3=8-5=3 dd44²=9²=9
SnSn = = dd11²+d²+d22²+d²+d33²=d²=d44²²
n-1n-1
Sn Sn == 9+1+1+99+1+1+9 = = 2020
4-14-1 3 3
Sn Sn =2.58=2.58
(calculator (calculator nn-1)-1)
![Page 14: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/14.jpg)
Roundout RulesRoundout RulesERLPM-page 47ERLPM-page 47
Example-last digit to be kept-nearest 10Example-last digit to be kept-nearest 10thth
4.614.614.624.624.644.644.65004.65004.664.664.674.674.684.684.694.69
Even Digit-sameEven Digit-sameOdd Digit-increase by 1Odd Digit-increase by 1This case becomes 4.6This case becomes 4.6If it was 4.7500 it would become 4.8If it was 4.7500 it would become 4.8
becomes 4.7
![Page 15: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/15.jpg)
MAT DensityMAT DensityManual Appendix E, page 4Manual Appendix E, page 4
SublotSublot1. = 96.01. = 96.02. = 97.02. = 97.03. = 99.03. = 99.04. = 100.04. = 100.0
x=98.0x=98.0SnSn=1.8=1.8
QQLL==x-Lx-L
SnSn
QQLL==98.0-96.398.0-96.3 = .9444 = .9444
1.81.8Section 110-Table l, N=4Section 110-Table l, N=4
PPLL=82=82
Section 110-02fSection 110-02f
Spec Tables 5Spec Tables 5
page 50 ERLPMpage 50 ERLPM
![Page 16: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/16.jpg)
Target Density 98.0 AchievedTarget Density 98.0 Achieved
SnSn=1.8 versus 1.3=1.8 versus 1.3
Acceptable QC Value
18%18%
PPL L = 82%= 82%
MAT DensityMAT Density
98.098.0
96.396.3
![Page 17: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/17.jpg)
Effect of Quality ControlEffect of Quality Control
90 PWL90 PWL
82 PWL82 PWL
SnSn = 1.8 = 1.8
SnSn = 1.3 = 1.3
Spec. pg 24Spec. pg 24
96.3%96.3% 98% 98% x x
![Page 18: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/18.jpg)
Air VoidsAir VoidsApp. D, page 3App. D, page 3
Sublot Sublot
1= 2.11= 2.1
2= 3.22= 3.2
3=2.53=2.5
4=6.04=6.0
X= 3.4X= 3.4
SnSn= 1.76= 1.76
Spec. page 5 - 0.65Spec. page 5 - 0.65
![Page 19: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/19.jpg)
QL = x-L = 3.4-2.0 = .7955
Sn 1.76
PPLL((table 1table 1) = 77%) = 77%
n=4n=4
QQUU= = U-xU-x = = 5-3.4 5-3.4 = .909= .909
SnSn 1.76 1.76
PPUU((table 1table 1) = 81%) = 81%
n=4n=4
PWL= PPWL= PLL + P + PUU-100-100
PWL= 77+81-100 = 58PWL= 77+81-100 = 58
![Page 20: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/20.jpg)
Air VoidsAir Voids
23%23%
58%58%
19%19%
22 3.43.4 55
PWL= PPWL= PLL + P + PUU-100-100
PWL= 77 + 81-100 =58PWL= 77 + 81-100 =58
![Page 21: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/21.jpg)
PaymentPayment
Spec-par 401-8.1a-page 29
MAT Density PWL=82
Air Voids PWL= 58
Lot Pay Factor
Air Voids- 1.4 x 58-12= 69.2%
Mat Density- 0.5 x 82+55= 96%
Use lower of 2 values- 69.2%
Lower valueLower value
![Page 22: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/22.jpg)
Joint DensityJoint DensityAppendix E, page 5Appendix E, page 5
93.3
95.0
97.0
96.0
X= 95.3
Sn= 1.58
QL= (95.3-93.3) = 1.2658
1.58
PL= 93
Spec. page 21 par. 401-5.2(b)(3) if < 71% there is a 5% penalty
Table 5Table 5
![Page 23: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/23.jpg)
Partial LotsPartial Lotsspec page 20spec page 20
Section P-401-5.1cSection P-401-5.1c
![Page 24: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/24.jpg)
Sample ProblemSample Problem
Flow-Appendix D, page 5Flow-Appendix D, page 5Partial lot situation-6 sublotsPartial lot situation-6 sublots
8.0, 8.2, 8.5, 8.2, 8.9, 9.18.0, 8.2, 8.5, 8.2, 8.9, 9.1X= 8.5X= 8.5
SnSn= 0.44= 0.44
QL= QL= x-Lx-L = = 8.5-8.08.5-8.0 = 1.1364; PL= 88 = 1.1364; PL= 88 Sn Sn 0.44 0.44
QU= QU= U-XU-X = = 16-8.516-8.5 = 18.75; PL= 100 = 18.75; PL= 100 SnSn 0.44 0.44
PWL= 88 + 100-100= 88<90PWL= 88 + 100-100= 88<90
Corrective Action! 401-5.2(b)(2)Corrective Action! 401-5.2(b)(2)
![Page 25: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/25.jpg)
OutliersOutliers
Spec -pg 23Spec -pg 23 401-5.2d401-5.2d
-pg 25-pg 25 401-5.3c401-5.3c
MAT Density and Air VoidsMAT Density and Air Voids
![Page 26: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/26.jpg)
![Page 27: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/27.jpg)
![Page 28: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/28.jpg)
Test for OutliersTest for Outliers
MAT DensityMAT Density
94.094.0
96.096.0
97.097.0
98.098.0
x= 96.2x= 96.2
Sn= 1.71Sn= 1.71
QL= QL= 96.2-96.396.2-96.3 = -.0585 = -.0585
1.711.71
PL= <50%PL= <50%
ASTM E 178, par. 4ASTM E 178, par. 4
TT11= (x-x= (x-x11)/)/SnSn
TT11= = 96.2-94 96.2-94 = 1.286= 1.286
1.711.71
![Page 29: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/29.jpg)
• Table 1-ASTM E 178Table 1-ASTM E 178
• N=4N=4
• Upper 5% significance level 1.463Upper 5% significance level 1.463
• Since 1.286<1.463 the 94.0 test value is Since 1.286<1.463 the 94.0 test value is not considered an outlier and is retained!not considered an outlier and is retained!
![Page 30: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/30.jpg)
Sample Problem-OutliersSample Problem-Outliers
Air VoidsAir Voids2.0, 4.8, 4.9, 5.02.0, 4.8, 4.9, 5.0X=4.2X=4.2Sn=1.45Sn=1.45
QQLL= = 4.2-2.04.2-2.0 = 1.5172; PL= 100 = 1.5172; PL= 100
1.451.45
QQUU= = 5-4.25-4.2 = 0.5517; PU= 69 = 0.5517; PU= 69
1.451.45PWL= (100+69)-100=69PWL= (100+69)-100=69ASTM E 178 par. 4ASTM E 178 par. 4
TTnn= (x-x= (x-x11)/)/SnSn = = 4.2-2.04.2-2.0 = 1.517 = 1.517
1.451.45Table 1, ASTM E 178, N=4, 5% significanceTable 1, ASTM E 178, N=4, 5% significanceT= 1.463<1.517 T= 1.463<1.517 therefore 2.0 is the outlier and it is discardedtherefore 2.0 is the outlier and it is discarded
![Page 31: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/31.jpg)
ResamplingResampling401-5.3 page 25401-5.3 page 25
MAT Density ONLYMAT Density ONLY(Appendix E-pg 4)(Appendix E-pg 4)Prior MAT Density- 96, 97, 99, 100Prior MAT Density- 96, 97, 99, 100PWL 82PWL 82
4 new cores 96, 96, 97, 984 new cores 96, 96, 97, 98AVG-all 8, 97.4AVG-all 8, 97.4Sn= Sn= 1.51 1.51
QQLL= = x-Lx-L = = 97.4-96.397.4-96.3 = .7337 = .7337
SnSn 1.51 1.51Table 1, N= 8Table 1, N= 8PWL= 77PWL= 77
![Page 32: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/32.jpg)
Questions?Questions?
![Page 33: Statistical Analysis Carl Steinhauer Consultant. Overview P 401 Test Results Statistical Analysis; PWL Estimate Verify Production Process: Payment.](https://reader036.fdocuments.us/reader036/viewer/2022062511/5519b50c55034660578b4761/html5/thumbnails/33.jpg)
Thanks!Thanks!