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ERLPM WorkshopERLPM WorkshopStatistical AnalysisStatistical Analysis
Carl SteinhauerCarl Steinhauer
ConsultantConsultant
35th Eastern Region 35th Eastern Region Annual Airports ConferenceAnnual Airports Conference
AnalysisAnalysis
% Taller than 5’-6” % Taller than 5’-6”
% between 5’-6” and 6’-6”% between 5’-6” and 6’-6”
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
OverviewOverview
P 401 Test ResultsP 401 Test Results
Statistical Analysis; PWL EstimateStatistical Analysis; PWL Estimate
Verify Production Process: PaymentVerify Production Process: Payment
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
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
Specific ProceduresSpecific Procedures
1.1. Sublots, Lots, Partial LotsSublots, Lots, Partial Lots
2.2. CalculationsCalculations
3.3. RetestingRetesting
4.4. OutliersOutliers
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
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
x+/- 1Sn=68%x+/- 1Sn=68%
x+/-2Sn+95%x+/-2Sn+95%
x+/-3Sn+99.7%x+/-3Sn+99.7%
xx
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
PWL Calculation ProceduresPWL Calculation ProceduresERLPM-page 48ERLPM-page 48
Section 110-AC 1505370-10CSection 110-AC 1505370-10C
Method for Computing PWL and ExamplesMethod for Computing PWL and Examples
Section 110-02Section 110-02
Spec. P401 Table 5: L and U Spec. LimitsSpec. P401 Table 5: L and U Spec. Limits
TEST PROPERTY
Pavements Designed for Aircraft Gross Weights of
60,000 Lbs. or More or Tire Pressures of 100 Psi or More
Pavements Designed for Aircraft Gross Weights Less
Than 60,000 Lbs. or Tire Pressures Less Than 100 Psi
Number of Blows 75 50
Specification Tolerance Limits
Specification Tolerance Limits
L U L U
Stability, minimum, pounds
1800 -- 1000 --
Flow, 0.01‑inch 8 16 8 20
Air Voids Total Mix, percent
2 5 2 5
Surface Course Mat Density, percent
96.3 [101.3] 96.3 [101.3]
Base Course Mat Density, percent
95.5 101.3]-- 95.5 [101.3]
Joint density, percent 93.3 -- 93.3 --
Table 5: Marshall Acceptance LimitsTable 5: Marshall Acceptance Limits
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
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)
Roundout RulesRoundout RulesERLPM-page 48ERLPM-page 48
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
MAT Density –One side density MAT Density –One side density acceptance (acceptance (Manual Appendix E, page 4)Manual 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
QQII==x-Lx-L
SnSn
QQII==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
Quality Index. See Section Quality Index. See Section 110-02f and Section 8 page 49 110-02f and Section 8 page 49 of ERLPM par 8.4.1 of ERLPM par 8.4.1
Spec Tables 5Spec Tables 5
ERLPM Table 4ERLPM Table 4
Mat Density -Two sided acceptance Mat Density -Two sided acceptance for densityfor densityx=98.0x=98.0SnSn=1.8=1.8QQuu= = U-x U-x (ERLPM page 50)(ERLPM page 50)
SnSnQQuu==101.3-98.0101.3-98.0 = 1.833 (101.3 found in spec Table 5) = 1.833 (101.3 found in spec Table 5)
1.81.8Determine PWL using ERLPM table 4. In column n=4 Determine PWL using ERLPM table 4. In column n=4
look up the Plook up the PLL value which corresponds to Qu=1.833 value which corresponds to Qu=1.833
Read PRead PLL= 100= 100
PWL calculation for two sided PWL calculation for two sided specificationspecification
PWL= PL + PU-100 PWL= PL + PU-100
(ERLPM page 50 par 8.5.2(ERLPM page 50 par 8.5.2 )
PWL= 82 + 100 – 100 = 82PWL= 82 + 100 – 100 = 82
Target Density 98.0 AchievedTarget Density 98.0 Achieved
SnSn=1.8 versus 1.3=1.8 versus 1.3
Acceptable QC Value as per P-401 spec. Table 5
18%18%
PPL L = 82%= 82%
MAT DensityMAT Density
98.098.0
96.396.3
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
101.3%101.3%
Effect of Quality ControlEffect of Quality Control
90 PWL90 PWL
82 PWL82 PWL
SnSn = 1.8 = 1.8
SnSn = 1.3 = 1.3
Spec. Table 5Spec. Table 5
96.3%96.3% 98% 98% x x
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= 1.76Spec. paragraph 401-3.2 Spec. paragraph 401-3.2 - 0.65- 0.65
QL = x-L = 3.4-2.0 = .7955
Sn 1.76
PPLL((table 4table 4) = 77%) = 77%
n=4n=4
QQUU= = U-xU-x = = 5-3.4 5-3.4 = .909= .909
SnSn 1.76 1.76
PPUU((table 4table 4) = 81%) = 81%
n=4n=4
PWL= PPWL= PLL + P + PUU-100-100
PWL= 77+81-100 = 58PWL= 77+81-100 = 58
page 51, 52 of page 51, 52 of ERLPM ERLPM
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
TABLE 6. PRICE ADJUSTMENT SCHEDULE 1
Percentage of Material WithinSpecification Limits (PWL)
Lot Pay Factor(Percent of Contract Unit Price)
96 – 100 106
90 – 95 PWL + 10
75 – 89 0.5 PWL + 55
55 – 74 1.4PWL – 12
Below 55 Reject 2
Payment – One side Payment – One side for densityfor density
TABLE 6. PRICE ADJUSTMENT SCHEDULE 1
Percentage of Material Within Specification Limits (PWL) Lot Pay Factor (Percent of Contract Unit Price)
93 – 100 103
90 – 93 PWL + 10
70 – 89 0.125PWL + 88.75
40 – 69 0.75PWL +45
Below 40 Reject 2
Payment – two sided for densityPayment – two sided for density
PaymentPayment
Spec-par 401-8.1a
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
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. par. 401-5.2(b)(3) if < 71% there is a 5% penalty
Table 5Table 5
Partial LotsPartial Lots
Section P-401-5.1cSection P-401-5.1c
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 (table 4 ERLPM n=6)table 4 ERLPM n=6)
Sn Sn 0.44 0.44QU= QU= U-XU-X = = 16-8.516-8.5 = 18.75; PL= 100 = 18.75; PL= 100
SnSn 0.44 0.44PWL= 88 + 100-100= 88<90PWL= 88 + 100-100= 88<90
Corrective Action! 401-5.2(b)(2)Corrective Action! 401-5.2(b)(2)
OutliersOutliers
Spec 401-5.2dSpec 401-5.2d
401-5.3c401-5.3c
MAT Density and Air VoidsMAT Density and Air Voids
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
• 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!
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
ResamplingResampling401-5.3 401-5.3
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 4, N= 8Table 4, N= 8PWL= 77PWL= 77
Questions?Questions?
Thanks!Thanks!
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