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32 nd Eastern Region Annual Airports Conference. ERLPM Workshop Statistical Analysis. Carl Steinhauer Consultant. Limit # of samples Statistical Analysis Estimate average and % within limits. Analysis % Taller than 5’-5” % between 5’-5” and 6’-5” Average Height. Overview.

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Erlpm workshop statistical analysis l.jpg

32nd Eastern Region

Annual Airports Conference

ERLPM WorkshopStatistical Analysis

Carl Steinhauer

Consultant


Slide2 l.jpg

Limit # of samples

Statistical Analysis

Estimate average and % within limits

Analysis

% Taller than 5’-5”

% between 5’-5” and 6’-5”

Average Height


Overview l.jpg
Overview

P 401 Test Results

Statistical Analysis; PWL Estimate

Verify Production Process: Payment


Theory l.jpg
Theory

  • Assumptions

  • Normal Distribution

  • Tools: Average and Standard Deviation

  • Percent Within Limits (PWL) Concept


Assumptions l.jpg
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


Specific procedures l.jpg
Specific Procedures

  • Sublots, Lots, Partial Lots

  • Calculations

  • Retesting

  • Outliers


Slide7 l.jpg

96 tests

n=100


Slide9 l.jpg

x

x+/- 1Sn=68%

x+/-2Sn+95%

x+/-3Sn+99.7%


Slide10 l.jpg

PWL-% of test result exceeding L

L

L=spec lower tolerance limit

eg. Mat density 96.3 for P401


Pwl calculation procedures erlpm page 47 l.jpg
PWL Calculation ProceduresERLPM-page 47

Section 110-AC 1505370-10C

Method for Computing PWL and Examples

Section 110-02

Spec. P401 Table 5: L and U Spec. Limits (page 24)



Given l.jpg
Given

x1=2

x2=4

x3=6

x4=8

X = 2+4+6+8 = 5

4


Slide14 l.jpg

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 = 9+1+1+9 = 20

4-1 3

Sn =2.58

(calculator n-1)


Roundout rules erlpm page 47 l.jpg
Roundout RulesERLPM-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 4.7500 it would become 4.8

becomes 4.7


Mat density one side density acceptance manual appendix e page 4 l.jpg
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

QL=x-L

Sn

QL=98.0-96.3 = .9444

1.8

Section 110-Table l, N=4

PL=82

Section 110-02f

Spec Tables 5

page 50 ERLPM


Mat density two sided acceptance for density l.jpg
Mat Density -Two sided acceptance for density

x=98.0

Sn=1.8

Qu=L-x

Sn

QL=101.3-98.0 = 1.833

1.8

Section 110-Table l, N=4

PL= 100


Pwl calculation for two sided specification l.jpg
PWL calculation for two sided specification

PWL= PL + PU-100

PWL= 82 + 100 – 100 = 82


Slide19 l.jpg

MAT Density

PL = 82%

Target Density 98.0 Achieved

Sn=1.8 versus 1.3

98.0

18%

96.3

Acceptable QC Value


Slide20 l.jpg

MAT Density

PL = 82%

Target Density 98.0 Achieved

Sn=1.8 versus 1.3

98.0

18%

96.3

101.3%

Acceptable QC Value


Effect of quality control l.jpg
Effect of Quality Control

Sn = 1.3

Spec. pg 24

Sn = 1.8

82 PWL

90 PWL

96.3%

98% x


Air voids app d page 3 l.jpg
Air VoidsApp. D, page 3

Sublot

1= 2.1

2= 3.2

3=2.5

4=6.0

X= 3.4

Sn= 1.76

Spec. page 5 - 0.65


Slide23 l.jpg

QL = x-L = 3.4-2.0 = .7955

Sn 1.76

PL(table 1) = 77%

n=4

QU= U-x = 5-3.4 = .909

Sn 1.76

PU(table 1) = 81%

n=4

PWL= PL + PU-100

PWL= 77+81-100 = 58


Air voids l.jpg
Air Voids

58%

23%

19%

2

5

3.4

PWL= PL + PU-100

PWL= 77 + 81-100 =58


Slide25 l.jpg

Payment – One side for density

TABLE 6. PRICE ADJUSTMENT SCHEDULE 1


Slide26 l.jpg

Payment – two sided for density

TABLE 6. PRICE ADJUSTMENT SCHEDULE 1


Payment l.jpg
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


Joint density appendix e page 5 l.jpg
Joint DensityAppendix 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 5


Partial lots spec page 20 l.jpg
Partial Lotsspec page 20

Section P-401-5.1c


Sample problem l.jpg
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 = 8.5-8.0 = 1.1364; PL= 88

Sn 0.44

QU= U-X = 16-8.5 = 18.75; PL= 100

Sn 0.44

PWL= 88 + 100-100= 88<90

Corrective Action! 401-5.2(b)(2)


Outliers l.jpg
Outliers

Spec -pg 23 401-5.2d

-pg 25 401-5.3c

MAT Density and Air Voids


Test for outliers l.jpg
Test for Outliers

MAT Density

94.0

96.0

97.0

98.0

x= 96.2

Sn= 1.71

QL= 96.2-96.3 = -.0585

1.71

PL= <50%

ASTM E 178, par. 4

T1= (x-x1)/Sn

T1= 96.2-94 = 1.286

1.71


Slide35 l.jpg

  • 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!


Sample problem outliers l.jpg
Sample Problem-Outliers

Air Voids

2.0, 4.8, 4.9, 5.0

X=4.2

Sn=1.45

QL= 4.2-2.0 = 1.5172; PL= 100

1.45

QU= 5-4.2 = 0.5517; PU= 69

1.45

PWL= (100+69)-100=69

ASTM E 178 par. 4

Tn= (x-x1)/Sn = 4.2-2.0 = 1.517

1.45

Table 1, ASTM E 178, N=4, 5% significance

T= 1.463<1.517

therefore 2.0 is the outlier and it is discarded


Resampling 401 5 3 page 25 l.jpg
Resampling401-5.3 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 = 97.4-96.3 = .7337

Sn 1.51

Table 1, N= 8

PWL= 77




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