1. ERLPM Workshop Statistical Analysis
34th Eastern Region
Annual Airports Conference
ERLPM Workshop Statistical Analysis
Carl Steinhauer
Consultant

2. Estimate average and % within limits
Limit # of samples
Statistical Analysis
Estimate average and % within limits
Analysis
% Taller than 5’-5”
% between 5’-5” and 6’-5”
Average Height

3. Statistical Analysis; PWL Estimate Verify Production Process: Payment
Overview
P 401 Test Results
Statistical Analysis; PWL Estimate
Verify Production Process: Payment

4. Theory Assumptions Normal Distribution
Tools: Average and Standard Deviation
Percent Within Limits (PWL) Concept

5. Assumptions
Limited # of test results Statistical Analysis Quality characteristics of large amount of material
Test result variability
Components:
materials
sampling-ERLPM
testing-ERLPM
Same Process
Random sampling-Lot, Sublot
Normal Distribution

6. Specific Procedures Sublots, Lots, Partial Lots Calculations Retesting
Outliers

7. 96 tests
n=100

9. x
x+/- 1Sn=68%
x+/-2Sn+95%
x+/-3Sn+99.7%

10. PWL-% of test result exceeding L
L=spec lower tolerance limit
eg. Mat density 96.3 for P401

11. PWL Calculation Procedures ERLPM-page 47
Section 110-AC C
Method for Computing PWL and Examples
Section
Spec. P401 Table 5: L and U Spec. Limits (page 24)

12. Table 5: Marshall Acceptance 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 L U
Stability, minimum, pounds
1800 --
1000
Flow, 0.01‑inch 8 16 20
Air Voids Total Mix, percent 2 5
Surface Course Mat Density, percent
96.3
[101.3]
Base Course Mat Density, percent
95.5
101.3]--
Joint density, percent
93.3

13. Given
x1=2
x2=4
x3=6
x4=8
X = = 5 4

14. Sn = d1²+d2²+d3²=d4² n-1 Sn = 9+1+1+9 = 20 4-1 3 Sn =2.58
X=5
d1=2-5=-3 d1²=9
d2=4-5=-1 d2²=1
d3=6-5=1 d3²=1
d4=8-5=3 d4²=9
Sn = d1²+d2²+d3²=d4²
n-1
Sn = = 20
Sn =2.58
(calculator n-1)

15. Roundout Rules ERLPM-page 47
Example-last digit to be kept-nearest 10th
4.61
4.62
4.64
4.6500
4.66
4.67
4.68
4.69
Even Digit-same
Odd Digit-increase by 1
This case becomes 4.6
If it was it would become 4.8
becomes 4.7

16. MAT Density –One side density acceptance (Manual Appendix E, page 4)
Sublot
1. = 96.0
2. = 97.0
3. = 99.0
4. = 100.0
x=98.0
Sn=1.8
QI=x-L Sn
QI= = .9444
1.8
Section 110-Table l, N=4
PL=82
Quality Index. See Section f and Section 8  page 48 of ERLPM par 8.4.1
Spec Tables 5
page 50 ERLPM

17. Mat Density -Two sided acceptance for density
x=98.0
Sn=1.8
Qu= U-x Sn
Qu= = 1.833
1.8
Section 110 (ERLPM page 48 par and page 50 ) -Table l, N=4
PL= 100

18. PWL calculation for two sided specification
PWL= PL + PU-100
(ERLPM page 49  par )
PWL= – 100 = 82

19. Target Density 98.0 Achieved Sn=1.8 versus 1.3
MAT Density
PL = 82%
98.0
18%
96.3
Target Density 98.0 Achieved
Sn=1.8 versus 1.3
Acceptable QC Value as per P-401 spec. pg 24 last par

20. Target Density 98.0 Achieved Sn=1.8 versus 1.3
MAT Density
PL = 82%
98.0
18%
96.3
Target Density 98.0 Achieved
Sn=1.8 versus 1.3
101.3%
Acceptable QC Value

21. Effect of Quality Control
Sn = 1.3
Spec. pg 24
Sn = 1.8
82 PWL
90 PWL
96.3%
98% x

22. Air Voids App. D, page 3 Sublot 1= 2.1 2= 3.2 3=2.5 4=6.0 X= 3.4
Sn= 1.76
Spec. page

23. QL = x-L = 3.4-2.0 = .7955 Sn 1.76 PL(table 1) = 77% n=4
QU= U-x = = .909 Sn
PU(table 1) = 81%
PWL= PL + PU-100
PWL= = 58
page 50  of ERLPM

24. Air Voids
58%
23%
19% 2 5
3.4
PWL= PL + PU-100
PWL= =58

25. Payment – One side for density
TABLE 6. PRICE ADJUSTMENT SCHEDULE 1
Percentage of Material Within
Specification 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

26. Payment – two sided for 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
40 – 69
0.75PWL +45
Below 40
Reject 2

27. Payment 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 value

28. Joint Density Appendix E, page 5
93.3
95.0
97.0
96.0
X= 95.3
Sn= 1.58
QL= ( ) =
1.58
PL= 93
Spec. page 21 par (b)(3) if < 71% there is a 5% penalty
Table 5

29. Partial Lots spec page 20
Section P c

30. Partial lot situation-6 sublots Corrective Action! 401-5.2(b)(2)
Sample Problem
Flow-Appendix D, page 5
Partial lot situation-6 sublots
8.0, 8.2, 8.5, 8.2, 8.9, 9.1
X= 8.5
Sn= 0.44
QL= x-L = = ; PL= 88 (table 1 ERLPM n=6) Sn
QU= U-X = = 18.75; PL= 100 Sn
PWL= = 88<90
Corrective Action! (b)(2)

31. MAT Density and Air Voids
Outliers
Spec -pg d
-pg c
MAT Density and Air Voids

34. Test for Outliers MAT Density 94.0 QL= 96.2-96.3 = -.0585 96.0 1.71
97.0
98.0
x= 96.2
Sn= 1.71
QL= =
1.71
PL= <50%
ASTM E 178, par. 4
T1= (x-x1)/Sn
T1= = 1.286
1.71

35. Table 1-ASTM E 178
N=4
Upper 5% significance level 1.463
Since 1.286<1.463 the 94.0 test value is not considered an outlier and is retained!

36. Sample Problem-Outliers
Air Voids
2.0, 4.8, 4.9, 5.0
X=4.2
Sn=1.45
QL= = ; PL= 100
1.45
QU= = ; PU= 69
PWL= (100+69)-100=69
ASTM E 178 par. 4
Tn= (x-x1)/Sn = = 1.517
Table 1, ASTM E 178, N=4, 5% significance
T= 1.463<1.517
therefore 2.0 is the outlier and it is discarded

37. Resampling 401-5.3 page 25 MAT Density ONLY (Appendix E-pg 4)
Prior MAT Density- 96, 97, 99, 100
PWL 82
4 new cores 96, 96, 97, 98
AVG-all 8, 97.4
Sn= 1.51
QL= x-L = = .7337 Sn
Table 1, N= 8
PWL= 77

38. Questions?

39. Thanks!