2 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.
3 INITIALIZATION TESTING Minimum of 10 testsInclude plant start-up testing1st Lot testing divided into 10 sublotsOptionally, initialization can be madeup of the first 2 lots of 5 sublots
4 INITIALIZATION TESTING Each set of asphalt testing includes:1 AIR VOID TEST1 AC CONTENT TEST3 ROADWAY DENSITY TESTS
5 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.
6 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”
7 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.
8 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 testingThe Contractor’s test results will be relied upon for acceptance and pay adjustments
9 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 testingODOT’s test results will be relied upon for acceptance and pay adjustments
10 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.
11 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.
12 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 resultsAt ODOT’s discretion, errant test results may be discarded. If replacement test results are available, they may be substituted for discarded test results
13 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.
14 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
15 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
16 GENERAL PROCEDURE STEP 1 U Calculate , the average of the differences between the paired tests
17 Where:Xp = The average of the differencebetween paired testsnp = Number of paired testsXc = The Contractor’s individual testresult for each sample.Xd = ODOT’s individual test result foreach sample.
18 GENERAL PROCEDURE STEP 2 U Calculate Sp, the standard deviation of the differences between the paired tests
19 Where:Sp = The Standard Deviation of thedifference between paired tests,np - 1 = Degrees of freedom, andXc, Xd, np, and Xp as previously defined.
20 GENERAL PROCEDURESTEP 3UCalculate tp, the paired-t teststatistic
21 tp = The paired-t test statistic, and 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 equationSimply put, if the result of the calculation is NEGATIVE, change it to a POSITIVE number
22 GENERAL PROCEDURE STEP 4 U Obtain the critical t-value, tcrit, from Table 1 in Appendix A using np-1 degrees of freedom
23 GENERAL PROCEDURE STEP 5 U Compare the calculated paired-t statistic (tp) to the critical t-value tcritUIf tp is less than tcrit, there is no statistically significant biasUIf tp is more than tcrit, there is a statistically significant bias
24 If tp is more than tcrit : Compare the testing bias (Xp) to the associated allowable testing bias (ATB) from the table in Appendix A:AC Quality Char ATB UnitsAC Content ± % by weightAir Voids ± % by volumeRoadway Density ± % of GmmNote: ATB’s for aggregates are for control charts and information only.
25 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
26 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.
27 EXAMPLE - % Air Voids Xc Xd TEST # 1 2 3 4 5 6 7 8 9 10 4.1 4.2 4.9 5.85.04.83.220.127.116.11.45.46.05.14.54.7
33 tp = < tcrit = 3.250Since 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.
34 ONGOING VALIDATION OF CONTRACTOR’S TEST METHODS
35 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.
36 ContractorDepartmentOne independentContractor: 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.
37 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.
39 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.
40 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.
41 F-test Calculate the mean of each test set. Xc = the mean of the Contractor’s resultsXc = individual Contractor resultnc = the number of Contractor resultsXd = the mean of the Department’s resultsXd = individual Department resultnd = the number of Department results
42 F-test Calculate the variance of each test set. = the variance of the Contractor’s resultsnc - 1 = degrees of freedom of Contractor results= the variance of the Department’s resultsnc - 1 = degrees of freedom of Department results
43 F-test or Calculate the F-statistic. Use the larger of the variances in the numerator so that the F-statistic is always greater than one.
44 F-testUDetermine Fcrit from the F-distribution table using a 0.01 significance levelUCompare the calculated F-statistic to the critical F-value FcritUIf F is less than Fcrit, the data is assumed from the same population.UIf F is more than Fcrit, the data is assumed from a different population
45 t-test Calculate the pooled variance, . Where nc + nd - 2 = pooled degrees of freedom
47 t-testUDetermine tcrit from the t-distribution table using a 0.01 significance level and the pooled degrees of freedomUCompare the calculated t-statistic to the critical t-value tcritUIf t is less than tcrit, the data is assumed from the same population.UIf t is more than tcrit, the data is assumed from a different population
48 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
49 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.
50 EXAMPLE - % Asphalt Content 1st Lot after Initialization – D2S Limits Test #XcXd114.184.08124.37134.27144.19154.21After initialization, ODOT and Contractor samples are no longer split samples but obtained independently
51 Step 1: Compute Averages Test #XcXd114.184.08124.37134.27144.19154.21Avg.4.244
52 Step 2: Compute D2S Comparison (D2S=0.30 from Appendix A Part 2 for Asphalt Cement content)Since is true, we assume that the test results come from the same population. The Contractor’s results are accepted.
53 EXAMPLE - % Asphalt Content 2nd Lot after Initialization – D2S Limits Test #XcXd124.21164.14174.27181920
54 Step 1: Compute Averages Test #XcXd124.21164.14174.27181920Avg.4.206
55 Step 2: Compute D2S Comparison (D2S=0.30 from Appendix A Part 2 for Asphalt Cement content)Since is true, we assume that the test results came from the same population. The Contractor’s results are accepted.
56 EXAMPLE - % Asphalt Content 3rd Lot after Initialization – Begin F & t Test #XcXd114.184.08164.14214.19124.374.21174.2722134.1118231419244.0015204.22254.50
61 Step 5: Compute F-statistic orFNumeratorDenominatorResult12.7620.36Note: Pick F with largest numerator (highest result).
62 Step 6: Pick Fcrit from F-distribution (2-tailed, =0.01) Table 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 thisn-11314152199343.343.243.1n-123138.196.92147.926.68157.706.48Not like this!
63 F ≤ Fcrit ? 2.75 ≤ 199 = True 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.