This section is based on Appendix A-IV “Percent within limits (PWL) for HMA Calculated Using Standard Deviation” from the AASHTO Recommended Practice “To Develop A Quality Control/Quality Assurance Plan for Hot Mix Asphalt”.
This module will cover procedures that are in common use for acceptance of HMA mixtures.
This concept is used to calculate percent within limits. Percent within limits is a tool to tell us how much of the hot mix being provided to the project fully meets the specification limits.
In this example – the average value is 5 % for both lots – but the variation as measured by the standard deviation is higher for lot 2. Therefore, the contractor will be paid less for lot two than for lot one.
In this example the variability as measured by the standard deviation is the same. But the average is different. Lot 2 will receive a lower pay than lot 1. The goal is to hit the target and to reduce variability. The result is a higher pay check when the mix is paid for.
The objective as we went through earlier – is to produce an HMA mix that exactly hits the center of the target and with every shot. The maximum pay comes from having accuracy and precision.
This concept is used to calculate percent within limits. Percent within limits is a tool to tell us how much of the hot mix being provided to the project fully meets the specification limits.
In the homework problems there are a couple of exercises for the students to work out. The following is a classroom exercise to work through with the students.
Where 1. Q(u) = Upper Quality Index 2. Q(L) = Lower Quality Index 3. X = average 4. USL = the Upper specification limit 5. LSL = the Lower specification limit 6. S = standard deviation
This is a listing of the steps associated with the computation of percent within limits.
The steps continued. The homework problems are set up to follow these steps.
Using the P u tables with the homework problems. The Price adjustment will be 0.97. Therefore, if the bid price is $40 per ton – the contractor will be paid $38.80 per ton for the HMA mix. This even though all of the test results were within the specification limits.
The conformal index is similar to the the standard deviation except that the deviation is calculated relative to the target value, not the mean of the lot. It can be used to estimate the size and incidence of the deviations (variations) from the target in the same way that the standard deviation measures the deviation from the mean of a lot.
Where 1. Q(u) = Upper Quality Index 2. Q(L) = Lower Quality Index 3. X = average 4. USL = the Upper specification limit 5. LSL = the Lower specification limit 6. CI = Conformal index
This is a listing of the steps associated with the computation of percent within limits using the conformal index. The steps are the same – with the exception of how the standard deviation is calculated.
The steps continued. The homework problems are set up to follow these steps.
Using the P u tables with the homework problems. The Price adjustment will be 0.90. Therefore, if the bid price is $40 per ton – the contractor will be paid $36.00 per ton for the HMA mix. This even though all of the test results were within the specification limits. Notice that the use of CI results in a higher price adjustment and less pay for the contactor.
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What you will learn….• The acceptance and compliance procedures used for hot mix asphaltConstruction QC/QA Acceptance 2
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ACCEPTANCE AND COMPLIANCE Did We Get What We Ordered?Construction QC/QA Acceptance 3
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How do we set the spec limits• They are set using typical industry standard deviations• Then allowing three standard deviations from the target• When setting the limits – the number of tests to be included in the lot are considered• The more tests – the tighter the specificationConstruction QC/QA Acceptance 4
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Typical Industry Standard Deviations• Based on extraction• Asphalt binder content: + 0.25 %• % Passing 4.75 mm (No. 4) and larger sieves: + 3 %• % Passing 2.36 (No 8) to .150 mm (No 100) sieves: + 2 %• Passing the 0.075 mm (No 200) sieve: + 0.7 %Construction QC/QA Acceptance 5
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Typical Industry Standard Deviations (cont.)• Compacted mix• Air voids:+ 1.0 %• Voids in Mineral Aggregate (VMA): + 1.5 %• Voids filled with asphalt (VFA): + 5 % Construction QC/QA Acceptance 6
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Equation• The following equation is used to set limits.• S(n) = s / n ½• Where – S(n) = standard deviation based on sample size n – S = standard deviation for material – n = sample sizeConstruction QC/QA Acceptance 7
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Example• Thus for asphalt binder content where 4 samples will make up the lot size the spec limits would be:• S = 0.25 and n = 4• S(n) = 0.25 / square root (4)• S(n) = 0.125• For three standard deviations the spec limits would be plus/minus 0.375 %.Construction QC/QA Acceptance 8
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Percent Within LimitsConstruction QC/QA Acceptance 9
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PWL Concept PWL = (PU + PL) - 100 In Terms of Area of the Distribution PL LSL PWL % AC USLConstruction PU QC/QA Acceptance 10
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Spec Percent Within Limits DataTarget Value 5.0 Lot X s PWLLimits ± 0.4 target 1 5.0 0.20 96 Lot 1 2 5.0 0.40 68 Lot 2 Upper limitLower limit4.2 4.6 5.0 5.4 5.8 Asphalt Binder ContentConstruction QC/QA Acceptance 11
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Percent Within LimitsTarget Value 5.0 Lot X s PWLLimits ± 0.4 1 5.0 0.20 96 target 2 4.8 0.20 84 Lot 2 Lot 1 Upper limitsLower limit4.2 4.6 5.0 5.4 5.8 Asphalt Binder ContentConstruction QC/QA Acceptance 12
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PWL ApproachTo get 100 % pay youneed to pay attention to both accuracy and precisionConstruction QC/QA Acceptance 13
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Steps• Sample the material using an appropriate random number system• Determine the average for the lot• Determine the standard deviation “s” for each lot• For Air voids, VMA and binder content calculate the upper and lower quality indices and the associated PWL• For in-place density, calculate the lower quality index and associated PWLConstruction QC/QA Acceptance 14
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Percent Within Limits Using Standard DeviationConstruction QC/QA Acceptance 15
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Equations - USL - x Q(u) = s - x - LSL Q(L) = sConstruction QC/QA Acceptance 17
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Acceptance Plan:Percent Within Limits (PWL) Approach1. Determine Random Sample Location Within Lot2. Make Measurements at Locations or on Material Samples3. Determine Average of Samples: n xi x =Σ n i=14. Determine Standard Deviation of Samples: (xi - x)2 Σ n s= i=1 n-1
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Acceptance Plan: Percent Within Limits (PWL) Approach5. Determine Upper Quality Index, Qu: (U - x) QU = s (x - L) QL =6. Determine sLower Quality Index, QL:7. Estimate PU and PL From Table Using Calculated QU and QL
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Example Problem• Percent passing 0.075 sieve – Test 1 : 4.1 – Test 2: 4.5 – Test 3: 4.8 – Test 4: 5.0 – Test 5: 5.1• Specification Target: 5.0 %• Allowable tolerance: See next slideConstruction QC/QA Acceptance 20
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Set Spec Limits• The typical standard deviation from industry is 0.7 %; therefore: – S = 0.7 and n = 5 – S(n) = 0.7 / square root (5) – S(n) = 0.7/2.236 = 0.313• For three standard deviations the spec limits would be + 0.94 %.• Therefore: – Upper spec limit = 5.94 % – Lower spec limit = 4.06 %Construction QC/QA Acceptance 21
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Compute values• The average is: – 4.72 %• Standard deviation for data is: – 0.43Construction QC/QA Acceptance 22
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Percent Within Limits Using Conformal IndexConstruction QC/QA Acceptance 25
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Equations - USL - x Q(u) = CI - x - LSL Q(L) = CIConstruction QC/QA Acceptance 26
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Acceptance Plan:Percent Within Limits (PWL) Approach1. Determine Random Sample Location Within Lot2. Make Measurements at Locations or on Material Samples3. Determine Average of Samples: n xi x =Σ n i=14. Determine Standard Deviation of Samples: (xi – spec requirement)2 Σ n Sci = i=1 n-1
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Acceptance Plan: Percent Within Limits (PWL) Approach5. Determine Upper Quality Index, Qu: (U - x) QU = S ci (x - L) QL =6. Determine S Lower Quality Index, QL: ci7. Estimate PU and PL From Table Using Calculated QU and QL
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Example Problem• Percent passing 0.075 sieve – Test 1 : 4.1 – Test 2: 4.5 – Test 3: 4.8 – Test 4: 5.0 – Test 5: 5.1• Specification Target: 5.0 %• Allowable tolerance: See next slideConstruction QC/QA Acceptance 29
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Set Spec Limits• The typical standard deviation from industry is 0.7 %; therefore: – S = 0.7 and n = 5 – S(n) = 0.7 / square root (5) – S(n) = 0.7/2.236 = 0.313• For three standard deviations the spec limits would be + 0.94 %.• Therefore: – Upper spec limit = 5.94 % – Lower spec limit = 4.06 %Construction QC/QA Acceptance 30
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Compute values• The average is: – 4.72 %• Conformal Index for data is: – 0.533Construction QC/QA Acceptance 31
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