INITIALIZATION AND ONGOING ACCEPTANCE

TESTING

In order to use the contractor’s test results for acceptance and payment, ODOT must ensure that the contractor’s test results compare favorably with their own.

Favorable comparability will be determined by means of paired testing of split samples.

INITIALIZATION TESTING

Minimum of 10 tests

1st Lot testing divided into 10 sublots

Optionally, initialization can be made

up of the first 2 lots of 5 sublots

Include plant start-up testing

Each set of asphalt testing includes:

INITIALIZATION TESTING

✓1 AIR VOID TEST

✓1 AC CONTENT TEST

✓3 ROADWAY DENSITY TESTS

At the conclusion of the sampling and associated

testing, a statistical “paired-t test” will be performed by ODOT using the pairs of initialization test data.

If there is a significant bias:

ODOT’s test results will be relied upon until the source of the bias

has been identified and corrected. The lack of bias must then be validated by further “paired-t

testing”

If Independent Evaluation requested:

The Contractor may request evaluation of the testing bias via three-way split sample testing with an independent laboratory.

ODOT will select the independent laboratory.

All initialization testing will be performed by all three laboratories using split samples.

If ODOT testing shows a significant bias:

●The Contractor will not be held responsible for any additional costs

incurred by ODOT in conjunction with the 3-way split-sample testing

●The Contractor’s test results will be relied upon for acceptance and pay

adjustments

If Contractor testing shows a significant bias:

●The Contractor shall reimburse ODOT for any additional costs incurred by

ODOT in conjunction with the 3-way split-sample testing

●ODOT’s test results will be relied upon for acceptance and pay adjustments

If paired-t testing validates the Contractor’s test methods, the Contractor’s test results

will be used for acceptance and pay adjustment subject to:

●ODOT will perform ongoing testing at a minimum frequency of 1 independent test

per lot.

●Ongoing process verification over time will be performed using the F-test and the

t-test.

If ODOT’s testing-bias Control Charts indicate an out-of-control condition

for testing bias:

Both the Contractor and ODOT will immediately investigate the probable

cause.

If the probable cause is identified and corrected or if the resulting bias is, in ODOT’s judgment, not likely to exceed

the Allowable Testing Bias:

Acceptance and pay adjustments will continue to be based on the Contractor’s

results

At ODOT’s discretion, errant test results may be discarded. If replacement test results are

available, they may be substituted for discarded test results

If the probable cause is not corrected or if the resulting bias is, in ODOT’s judgment, likely to exceed the allowable testing bias:

All subsequent testing will be paired testing until the source of the

unaccepatable testing bias is corrected.

During this period, acceptance and pay adjustments will be based on ODOT’s test

results.

GUIDELINES FOR INITIAL VALIDATION OF CONTRACTOR’S TEST METHODS

●A paired test shall consist of 2 separate tests by ODOT and the

Contractor on a split sample

PAIRED TESTING

On split samples test:●Air Voids

●Asphalt Cement Content

For Roadway Densities, perform paired tests on the same cores. The

first lab to test the cores should make sure to oven-dry the cores at

140°F instead of 230°F

GENERAL PROCEDURE

Calculate , the average of thedifferences between the paired tests

pX

STEP 1

Where:

np = Number of paired tests

Xd = ODOT’s individual test result for

Xp = The average of the differencebetween paired tests

Xc = The Contractor’s individual test result for each sample.

each sample.

p

n

1 idc

pn

)X(XX

p

GENERAL PROCEDURE

Calculate Sp, the standard deviation of the differences between the

paired tests

STEP 2

Where:

Sp = The Standard Deviation of the

np - 1 = Degrees of freedom, and

difference between paired tests,

Xc, Xd, np, and Xp as previously defined.

1n

XX(XS

p

n

1i

pdc

p

p

2)

GENERAL PROCEDURE

Calculate tp, the paired-t teststatistic

STEP 3

Where:

tp = The paired-t test statistic, andnp, Xp, and Sp as previously

defined. The vertical lines on either side of the equation indicate the need to take the ABSOLUTE VALUE of the

equation

Simply put, if the result of the calculation is NEGATIVE, change it to

a POSITIVE number

p

p

pp S

Xnt

GENERAL PROCEDURE

Obtain the critical t-value, tcrit, from Table 1 in Appendix A

using np-1 degrees of freedom

STEP 4

GENERAL PROCEDURE

Compare the calculated paired-t statistic (tp) to the critical t-value tcrit

STEP 5

If tp is less than tcrit, there is no statistically significant bias

If tp is more than tcrit, there is a statistically significant bias

Compare the testing bias (Xp) to the associated allowable testing bias (ATB) from

the table in Appendix A:

If tp is more than tcrit

:

AC Quality Char. ATB Units

AC Content ± 0.15 % by weight Air Voids ± 0.50 % by volume

Roadway Density ± 0.50 % of Gmm

Note: ATB’s for aggregates are for control charts and

information only.

If the magnitude of Xp is less than the magnitude of the corresponding ATB, the Contractor’s bias is statistically,

but not practically significant.

Contractor test results shall then be relied upon for acceptance and pay

adjustments

If the magnitude of Xp is greater than or equal to the magnitude of the

corresponding ATB, the Contractor’s bias is practically significant and unacceptable.

Contractor test results shall not be relied upon until certified by a qualified

independent calibration specialist and validated through further paired-t testing.

EXAMPLE - % Air Voids

TEST #

1 2 3 4 5 6 7 8 9

10

Xc 4.14.24.95.85.04.83.75.14.9

4.5

Xd 3.94.45.46.05.14.53.95.44.7

4.7

Step 1 – Average DifferencesTEST #

1 2 3 4 5 6 7 8 9

10

Xc 4.14.24.95.85.04.83.75.14.9

4.5

Xd 3.94.45.46.05.14.53.95.44.7

4.7

Xc - Xd

0.2

-0.2-0.5-0.2-0.10.3

-0.2-0.3

0.2-0.2

Xp = -0.1

Step 2 – Standard DeviationTEST #

1 2 3 4 5 6 7 8 9

10

Xp -0.1-0.1-0.1-0.1-0.1-0.1-0.1-0.1-0.1

-0.1

Xc - Xd - Xp 0.3

-0.1-0.4-0.1

0.00.4

-0.1-0.2

0.3-0.1

Xc - Xd

0.2

-0.2-0.5-0.2-0.10.3

-0.2-0.3

0.2-0.2

(Xc - Xd - Xp)2 = 0.58

(Xc - Xd - Xp)2

0.090.010.160.010.000.160.010.040.09

0.01

Sp = 0.25386

1n

XX(XS

p

n

1i

pdc

p

p

2)

110

0.58Sp

tp = 1.246

p

p

pp S

Xnt

0.25386

0.1-10tp

Degrees ofFreedom(np – 1)

Criticalt-value

(tcrit)

9.925

3.250

23 5.8414 4.6045 4.0326 3.7077 3.4998 3.3559

3.16910

tp = 1.246 < tcrit = 3.250

Since tp < tcrit, there is no statistical bias. Therefore the contractor’s

tests on this quality characteristic are valid and will be relied upon for acceptance and pay adjustments.

ONGOING VALIDATION OF CONTRACTOR’S TEST METHODS

GUIDELINES FOR ONGOING VALIDATION OF CONTRACTOR’S TEST METHODS

●Ongoing process verification over time will be performed using the F-test

and the t-test.

●The F-test provides a method for comparing the variances of the two data

sets.

● The t-test provides a method for comparing the means of the two data

sets.

Contractor

Department

One independent

Contractor: Collect samples to split and test ¼, discard ¼, store 2nd half.

ODOT: Collect one sample per lot, independent of Contractor’s samples.

Test ¼, discard ¼, store 2nd half.

GUIDELINES FOR ONGOING VALIDATION OF CONTRACTOR’S TEST METHODS

●First two lots do not yield enough data for F-test and t-test.

●These lots will be validated by comparing to D2S limits.

● If │Xc – Xd │≤ D2S limit, assumed from same population – Contractor’s accepted.

● If │Xc – Xd │> D2S limit, assumed from different populations – ODOT’s used.

D2S LIMITS

Quality Characteristic D2S Limits

Asphalt Cement Content 0.30%

Air Voids (Lab Molded) 1.40%

Roadway Density 1.40%

THIRD - FIFTH LOT AFTER INITIALIZATION

●Using the F-test and t-test for process verification.

●Use all data after Initialization, including that used for D2S comparisons.

● By third lot after Initialization there should be 15 contractor results and 3

ODOT results.

SIXTH LOTS & FOLLOWING AFTER INITIALIZATION

●Still using the F-test and t-test for process verification.

●Use the current lot results plus the previous four for a total of five lots.

● Each of these analyses should include 25 contractor results and 5 ODOT results.

F-test● Calculate the mean of each test set.

c

cc

n

XX

d

dd

n

XX

Xc = the mean of the Contractor’s results

Xd = the mean of the Department’s results

Xc = individual Contractor result

Xd = individual Department result

nc = the number of Contractor results

nd = the number of Department results

F-test● Calculate the variance of each test

set.

nc - 1 = degrees of freedom of Contractor results

= the variance of the Contractor’s results2cs

nc - 1 = degrees of freedom of Department results

= the variance of the Department’s results2ds

1n

)XX(s

c

2cc2

c

1n

)XX(s

d

2dd2

d

F-test● Calculate the F-statistic.

Use the larger of the variances in the numerator so that the F-statistic is always greater than one.

2d

2c

s

sF

2c

2d

s

sF or

Compare the calculated F-statistic to the critical F-value Fcrit

If F is less than Fcrit, the data is assumed from the same population.

If F is more than Fcrit, the data is assumed from a different population

F-test Determine Fcrit from the F-distribution

table using a 0.01 significance level

t-test

● Calculate the pooled variance, .

Where nc + nd - 2 = pooled degrees of freedom

2ps

2nn

1)(ns1)(nss

dc

d2dc

2c2

p

t-test● Calculate the t-statistic.

d

sp

c

2p

dc

n

s

n

s

XXt

Compare the calculated t-statistic to the critical t-value tcrit

If t is less than tcrit, the data is assumed from the same population.

If t is more than tcrit, the data is assumed from a different population

t-test Determine tcrit from the t-distribution

table using a 0.01 significance level and the pooled degrees of freedom

Both the F-test and the t-test must show the results to be from the same population to

continue accepting the Contractor’s results

If either test shows the results to be from different

populations, ODOT will test the remaining half of

the Contractor’s split samples for acceptance until the reason for the difference is resolved.

EXAMPLE - % Asphalt Content1st Lot after Initialization – D2S Limits

Test # Xc Xd

11 4.18 4.08

12 4.37

13 4.27

14 4.19

15 4.21

After initialization, ODOT and Contractor samples are no longer split

samples but obtained independently

Step 1: Compute Averages

Test # Xc Xd

11 4.18 4.08

12 4.37

13 4.27

14 4.19

15 4.21

Avg. 4.244 4.08

Step 2: Compute D2S Comparison

S2DX-X dc

30.008.4244.4 - (D2S=0.30 from

Appendix A Part 2 for Asphalt Cement content)

True 30.0164.0

● Since is true, we assume that the test results come from the same population.

The Contractor’s results are accepted.

D2SX- dc X

EXAMPLE - % Asphalt Content2nd Lot after Initialization – D2S Limits

Test # Xc Xd

12 4.21

16 4.14

17 4.27

18 4.21

19 4.14

20 4.27

Step 1: Compute Averages

Test # Xc Xd

12 4.21

16 4.14

17 4.27

18 4.21

19 4.14

20 4.27

Avg. 4.206 4.21

Step 2: Compute D2S Comparison

30.021.4206.4 -

True 30.0004.0

● Since is true, we assume that the test results came from the same population.

The Contractor’s results are accepted.

D2SXX dc

S2DX-X dc (D2S=0.30 from

Appendix A Part 2 for Asphalt

Cement content)

EXAMPLE - % Asphalt Content3rd Lot after Initialization – Begin F & t

Test #

Xc XdTest

#Xc

Test #

Xc

11 4.18 4.08 16 4.14 21 4.19

12 4.37 4.21 17 4.27 22 4.21

13 4.27 4.11 18 4.21 23 4.14

14 4.19 19 4.14 24 4.00

15 4.21 20 4.22 25 4.50

Step 1: Compute Mean for Each Set

c

cc

n

XX

d

dd

n

XX

4.224.219333315

63.29Xc

4.134.13333333

12.40Xd

Step 2: Compute s2 (Variance) for Each Set

1n

)XX(s

c

2cc2

c

1n

)XX(s

d

2dd2

d

Step 3: Compute sc2

Test # Xc(Xc-Xc)2

11

12

4.08

4.21

0.0025

0.0064

Sum

Sum/(nc-1)

25 4.50 0.0784

63.29 0.1797

0.1797 / (15-1)

0.01284sc2

Xc ≈ 4.22

Step 4: Compute sd

Test # Xd (Xd-Xd)2

11 4.08 0.0025

12 4.21 0.0064

13 4.11 0.0004

Sum 0.0093

Sum/(nd-1)

0.0093/(3-1)

sd 0.00465

2

2

Xd ≈ 4.13

Step 5: Compute F-statistic

2d

2c

s

sF

2c

2d

s

sF or

F NumeratorDenominat

orResult

1 0.01284 0.00465 2.76

2 0.00465 0.01284 0.36

Note: Pick F with largest numerator (highest result).

Step 6: Pick Fcrit from F-distribution (2-tailed, =0.01) Table

n-1 13 14 15

2 199 199 199

3 43.3 43.2 43.1

n-1 2 3

13 8.19 6.92

14 7.92 6.68

15 7.70 6.48

For this example, contractor variance

was in the numerator with 14 degrees of

freedom and ODOT’s variance was in the denominator with 2

degrees of freedom. Read the table like this

Not like this!

Step 7: Perform F-test

● Since F-test is true, we must perform

the T-test.

● Had F-test been false, the tests would not have come from the same population. The

Contractor’s results would not be accepted.

F ≤ Fcrit ? 2.75 ≤ 199 = True

Step 8: Compute Pooled Variance

2ps

2nn

1)(ns1)(nss

dc

d2dc

2c2

p

2315

1)0.00465(31)-0.01284(15S2

p

0.0118s2p

Step 9: Compute t-statistic

d

sp

c

2p

dc

n

s

n

s

XXt

30.0118

150.0118

4.134.22t

1.31t

Note: Without rounding, t ≈ 1.25.

Step 10: Pick tcrit from t-distribution (2-tailed, =0.01) Table

DF tcrit

15 2.947

16 2.921

17 2.898

• Degrees of freedom = nc + nd – 2

DF = 15 + 3 – 2 = 16

Step 11: Perform t-test

● Since both t-test and F-test are true, we assume

that the test results came from the same population. The Contractor’s results are

accepted.

t ≤ tcrit ? 1.31 ≤ 2.921 = True