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

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

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

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

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 Sublots, Lots, Partial Lots Calculations Retesting Outliers

96 tests n=100

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

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

PWL Calculation Procedures ERLPM-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)

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

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

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 = 9+1+1+9 = 20 4-1 3 Sn =2.58 (calculator n-1)

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 4.7500 it would become 4.8 becomes 4.7

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=98.0-96.3 = .9444 1.8 Section 110-Table l, N=4 PL=82 Quality Index. See Section 110-02f and Section 8  page 48 of ERLPM par 8.4.1 Spec Tables 5 page 50 ERLPM

Mat Density -Two sided acceptance for density x=98.0 Sn=1.8 Qu= U-x Sn Qu=101.3-98.0 = 1.833 1.8 Section 110 (ERLPM page 48 par 8.4.2. and page 50 ) -Table l, N=4 PL= 100

PWL calculation for two sided specification PWL= PL + PU-100 (ERLPM page 49  par 8.5.2 ) PWL= 82 + 100 – 100 = 82

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

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

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 Sublot 1= 2.1 2= 3.2 3=2.5 4=6.0 X= 3.4 Sn= 1.76 Spec. page 5 - 0.65

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% PWL= PL + PU-100 PWL= 77+81-100 = 58 page 50  of ERLPM

Air Voids 58% 23% 19% 2 5 3.4 PWL= PL + PU-100 PWL= 77 + 81-100 =58

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

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 + 88.75 40 – 69 0.75PWL +45 Below 40 Reject 2

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 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 Section P-401-5.1c

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 = 8.5-8.0 = 1.1364; PL= 88 (table 1 ERLPM n=6) 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)

MAT Density and Air Voids Outliers Spec -pg 23 401-5.2d -pg 25 401-5.3c MAT Density and Air Voids

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= 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

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 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 PWL= (100+69)-100=69 ASTM E 178 par. 4 Tn= (x-x1)/Sn = 4.2-2.0 = 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

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 = 97.4-96.3 = .7337 Sn 1.51 Table 1, N= 8 PWL= 77

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