Development and Implementation of a PerformanceRelated Specification for I65 Tennessee: Final Report
Chapter 3. Development of the PerformanceRelated Specification
Selection of Acceptance Quality Characteristics
The following AQCs can be considered directly in the PaveSpec PRS methodology for JPCPs:
 Concrete strength.
 Slab thickness.
 Initial smoothness.
 Entrainedair content.
 Percent consolidation around dowel bars.
These AQCs were found to affect pavement performance and are under the control of the paving contractor. TDOT includes concrete strength, slab thickness, initial smoothness, and entrainedair content in their existing method specifications. After significant discussion, TDOT decided to use the following AQCs and test methods in the PRS for I65:
 Concrete strength: The compressive strength at 28 days is the standard quality characteristic used, and this was the logical value to use in the PRS.
 Slab thickness: Typically measured by cores, and TDOT had an interest in specifying the impact echo procedure for this project.
 Initial smoothness: The Rainhart profilograph with a 0.1in. (2.5 mm) blanking band is specified for use on this project.
TDOT Concrete Pavement Specifications
The current method specifications include the following items:
 Slab thickness: Measured by coring the pavement at 1,000ft (304.8 m) intervals.
 PCC strength: Measured by taking cylinders at the paving site and curing them for 28 days to determine their compressive strength. One batch of PCC is taken each 400 yd^{3} (305.8 m^{3}), for a minimum of two cylinders.
 Smoothness/profile: Measured by testing each wheelpath using the Rainhart profilograph with a 0.1in. (2.5 mm) blanking band.
Details of measurement and pay are provided later in this chapter.
Establishment of AsDesigned Target Values
PRS differs from other QC specifications in that target means and standard deviations are specified, not minimums. The target means and standard deviations of the AQCs are those values that, if achieved by the contractor for an asconstructed lot, will be paid for at 100 percent of the bid price. Considerable discussion went into the selection of the asdesigned target values. Since this would be the first PRS project conducted in Tennessee, it was decided that the target levels set in the specification should not significantly exceed the level of quality being achieved under the current method specification. Given the magnitude of incentives, it was considered that the contractor may exceed the targets, but forcing an increase in quality by raising the target quality level (e.g., increasing PCC strength target) was not desired in this project. Of course, depending on the results of this project, TDOT may modify the target values in the future.
To determine the level of quality currently being achieved, historical data from three projects were obtained. A summary is given in table 1. These results show the following:
 Compressive strength of PCC ranged from 5,247 to 6,432 lbf/in^{2} (36.18 to 44.35 MPa) with a mean of 5,908 lbf/in^{2} (40.73 MPa).
 Compressive strength standard deviation of PCC ranged from 315 to 892 lbf/in^{2} (2,171.8 kPa to 6,150.1 kPa) with a mean (computed from the mean of the variances) of 655 lbf/in^{2} (4,516.1 kPa).
 Slab thickness data were not sufficient to analyze.
 Slab thickness standard deviation was available on one project with a value of 0.11 in. (2.8 mm).
 Profile index (PI) ranged from 2.53 to 2.55 in./mi (39.91 to 40.23 mm/km) with a mean of 2.54 in./mi (40.07 mm/km) (may have been measured after diamond grinding).
 PI standard deviation of thickness ranged from 0.71 to 0.88 in./mi (11.20 to 13.88 mm/km) with a mean of 0.8 in./mi (12.62 mm/km).
Table 1. Summary of Data From Three Previous Portland Cement Concrete Projects
Attribute 
Project #1 
Project #2 
Project #3 
Tennessee Department of Transportation
Identification 
S.P. 33003415404 
IM402(71)87, 57001817244 
NHI751(95)3, 33005316144 
Location 
I24, Hamilton County 
I40, Madison & Henderson Counties 
I75, Hamilton County 
Approximate length, mi 
2.76 
8.02 
3.2 
Project period 
1997–2000 
1997 
19992001 
28day compressive strength, lbf/in^{2} 
Field average 
6,432 
5,247 
6,046 

Field standard deviation 
892 
315 
625 

Specifications 
Min. 3,000 
Min. 3,000 
Min. 3,000 
Thickness, in. 
Field average 
NA 
NA 
12.04 

Field standard deviation 
NA 
NA 
0.11 

Specifications 
NA 
NA 
12 
Air content, % 
Field average 
5.46 
5.11 
5.14 

Field standard deviation 
0.51 
0.11 
0.44 

Specifications 
3 to 8 
3 to 8 
3 to 8 
Profile index, in./mi 
Field average 
2.55 
NA 
2.53 

Field standard deviation 
0.88 
NA 
0.71 

Specifications 
5 
NA 
4 
1 mi = 1.61 km; 1 lbf/in^{2} = 6.89 kPa; 1 in. = 25.4 mm; 1 in./mi = 16 mm/km 
If the TDOT mean and standard deviation targets for each of the AQCs used for pay adjustment are met, the agency will pay 100 percent of the bid price. Table 2 shows target quality levels (mean and standard deviations) selected after examination of results achieved on previous PCC projects and significant discussion about the impacts of selection of AQC target levels.
Slab Thickness. The logical target mean is the design thickness (13 in. [330.2 mm). Specification of anything different would be inappropriate because this is what is called for in the design at a given level of reliability. Requiring more than the mean thickness would artificially add reliability to the design and is not recommended. The target standard deviation of thickness was set at 0.5 in. (12.7 mm), which is higher variability than a previous project target that appeared to be unreasonably low (0.11 in. [2.8 mm]).
PCC Strength. Compressive strength being achieved on previous projects is shown in table 1. The typical values presented previously were considered, and a somewhat lower value of 4,500 lbf/in^{2} (31.03 MPa) was selected as representing the quality level desired by TDOT at 100 percent of PF. The standard deviation of PCC compressive strength was set slightly lower, at 500 lbf/in^{2} (3,447 kPa), than past historical data indicated (655 lbf/in^{2} [4,516 kPa]).
Smoothness (or Profile Index). Values of the PI achieved on two previous projects showed approximately 2.5 in./mi (39.44 mm/km) using the Rainhart profilograph with a 0.1in. (2.5 mm) blanking band. This value was considered too low, and may require significant, undesirable grinding. Therefore, a value of 7.0 in. (177.8 mm) was selected as the target mean. The standard deviation of PI was set at 1.0 in./mi (15.78 mm/km), slightly higher than past data (0.8 in./mi [12.6 mm/km]).
Table 2. Lot Acceptance Quality Characteristic Target Lot Mean and Standard Deviation Selected for I65 Project
Acceptance Quality Characteristic 
Lot Target Values 
Mean 
Standard Deviation 
Slab thickness, in. 
13.0 
0.5^{(1)} 
Compressive strength: 28 days, lbf/in^{2} 
4,500 
500^{(2)} 
Initial profile index (with 0.1 in. blanking band), in./mi 
7.0 
1.0^{(3)} 
1 in. = 25.4 mm; 1 lbf/in^{2} = 6.89 kPa; 1 in./mi = 16 mm/km 
 Thickness: mean and standard deviation computed from independent cores (one core per sublot).
 Compressive strength: mean and standard deviation computed from averages of two replicate cylinders taken at one location per sublot.
 Profile index: mean and standard deviation computed from averages of inside and outside wheelpaths of each 500ft (152.4 m) section in the lot measured prior to any grinding.
TDOT Pavement Performance Indicators
The PaveSpec PRS uses inputs from the asdesigned target lot and predicts performance over a designated analysis period. The key performance indicators included in PaveSpec are the following for JPCP:
 Slab transverse fatigue cracking, percent slabs.
 Joint faulting, inches.
 Joint spalling, percent joints.
 PI (at 0.1in. [2.5 mm] blanking band).
Definitions of these distress types are provided in reference 4.
Inputs Used for PaveSpec 3.0
The following section provides information on the critical terminal values for use in PaveSpec 3.0 analysis of pavement life.
General Information.
Project Number: I65 from Old Hickory Boulevard at LM 91.55 to CSX Railroad at LM 95.03
Location: Nashville, Tennessee
Project length: 3.478 miles
Number of lanes: Five in each direction
Pavement Design Features. Table 3 shows the design feature inputs used in PaveSpec 3.0.
Traffic Loadings. Table 4 shows the traffic loading inputs used in PaveSpec 3.0. The listed traffic inputs result in a projected 92 million equivalent singleaxle loads (ESALs) in the design lane over the 20year analysis period.
Climate. Table 5 shows the climatic inputs used in PaveSpec.
Table 3. Design Feature Inputs Used in PaveSpec 3.0
Design Feature 
Value 
Data Source/ Comment 
Design life 
20 
Ok 
Pavement type 
Jointed plain concrete 
Ok 
Dowel bar diameter 
1.625 in. 
Ok 
Transverse joint spacing 
15 ft 
Ok 
PCC modulus of elasticity 
4,461,750 lbf/in^{2} 
Ok 
Transverse joint sealant type 
Silicone 
Ok 
Modulus of subgrade reaction (kvalue) 
126 lbf/in^{2}/in. 
Ok 
Water–cementitious materials ratio 
0.42 
Ok 
% Subgrade material pass sieve #200 
75 
Ok 
Base type 
Permeableasphalttreated aggregate 
Ok 
Base permeability 
Yes 
Ok 
Base thickness 
4in. asphalttreated permeable over 4in. aggregate separator layer 
Ok 
Base modulus of elasticity 
100,000 lbf/in^{2} typ. at 70 °F 
Ok 
PCCBase Interface 
Bonded 
Ok 
Base erodibility factor (1 = totally nonerodable material, 5 = granular) 
1.5 permeable 
Ok 
1 in. = 25.4 mm; 1 ft = 0.305 m; 1 lbf/in^{2} = 6.89 kPa 
Table 4. Traffic Inputs Used in PaveSpec
Item 
Value 
Data Source/ Comment 
Average daily traffic (both directions) 
98,770 
2004 estimate 
Growth type 
Linear 
Ok 
Growth rate 
2.7% 
Ok 
Directional factor 
50% 
Ok 
Percent trucks 
20% 
Ok 
Percent trucks in outer lane 
60% 
Ok 
Avg. truckload equivalency factor 
1.78 ESALs/truck 
Ok 
ESAL = equivalent singleaxle load 
Table 5. Climatic Inputs Used in PaveSpec 3.0
Item 
Value 
Data Source/ Comment 
Average annual freezing index 
226 per degree F 
Ok 
Average annual precipitation 
56 in. 
Ok 
Average annual air freeze–thaw cycles 
60 air freeze–thaw cycles 
Ok 
Average annual # of days > 90 °F 
42 days 
Ok 
Climate zone 
Wet–freeze 
Ok 
1 in. = 25.4 mm; 1 ft = 0.305 m; 1 lbf/in^{2} = 6.89 kPa 
M&R Plan. The following M&R activities were established based on discussions with TDOT staff.
Maintenance Plan Summary:
 Reseal 50 percent of the transverse joints every 10 years.
 Reseal 100 percent of the longitudinal joints every 10 years.
 Seal 100 percent of the transverse cracks every 5 years.
Localized Rehabilitation Plan Summary:
 Always apply 100 percent slab replacements to cracked slabs.
 If spalled joints exceed 30 percent, then apply partialdepth repairs to 100 percent of slabs.
Sublot Failure Thresholds:
 Consider the sublot failed if cumulative percent cracked slabs exceeds 20 percent.
 Consider the sublot failed if average transverse joint faulting exceeds 0.15 in. (3.8 mm).
 Consider the sublot failed if International Roughness Index (IRI) exceeds 175 in./mi (2,760 mm/km).
 Consider the sublot failed if cumulative percent joints spalled exceeds 30 percent.
If 20 percent of the sublots are failed, apply the global rehabilitation activities in table 6.
Table 6. Global Rehabilitation Activities If 20 Percent of Sublots Are Failed
Global Rehabilitation Activity 
Activities 
Prior to Phase I 
Repair 100% of outstanding spalled joints with partialdepth repairs.
Repair 100% of outstanding cracked slabs with full slab replacements 
Phase I (diamond grinding) 
Assumed life: 10 years
Starting IRI: 50 in./mi
Ending IRI: 175 in./mi 
Phase II (diamond grinding) 
Assumed life: 10 years
Starting IRI: 50 in./mi
Ending IRI: 175 in./mi 
Phase III (asphalt concrete overlay) 
Assumed Life: 10 years
Starting IRI: 50 in./mi
Ending IRI: 175 in./mi 
Phase IV (asphalt concrete overlay) 
Assumed life: 10 years
Starting IRI: 50 in./mi
Ending IRI: 175 in./mi 
1 in./mi = 16 mm/km 
This selection of 20 percent is important in that it triggers overall lot rehabilitation if 20 percent of the sublots reach a terminal cracking, faulting, or IRI. Thus, more variability within the project will result in 20 percent of sublots failing in cracking, faulting, or IRI earlier.
Unit Costs. Table 7 shows the unit costs estimated for this project used in PaveSpec.
Table 7. Design Feature Inputs Used in PaveSpec 3.0
Cost Item 
Cost (in 2004 Dollars) 
Transverse joint sealing 
1.20/ft 
Longitudinal joint sealing 
0.80/ft 
Transverse crack sealing 
1.20/ft 
Local: Partialdepth repairs of transverse joints* 
70.00/yd^{2} 
Local: Full slab replacements 
75.00/yd^{2} 
Local: Partial slab replacements 
105.00/yd^{2} 
Global: Asphalt concrete overlay 
9.00 per yd^{2} 
Global: Diamond grinding 
5.25 per yd^{2} 
% user cost 
2 (provides about the right amount of user impact on pay factor) 
Estimated bid price 
$31.95 per yd^{2} (contractors bid for 13in. jointed plain concrete pavement) 
1 ft = 0.305 m; 1 yd^{2} = 0.836 m^{2}
*Width of partialdepth repair of transverse joints = 6 in. across joint. 
Definitions of Lots and Sublots
The PRS AQCs of thickness, strength, and PI are measured within each sublot. All values measured within the lot are combined to compute a mean and standard deviation of the lot. The pay adjustment for a given lot is then computed from these values. Pay is determined on a lotbylot basis, not by the sublot.
There must be precise and easily understood definitions of lots and sublots, as ambiguity can cause significant problems in the field. These definitions required perhaps more discussion among the TDOT and project staff than any other item. Thus, sublots were set at a constant 500ft (152.4 m) interval to provide simple, consistent testing methods. Sublot boundaries are marked and maintained until finalizing the payment computation. Each lot is divided into a minimum of three sublots for sampling and testing purposes. Markers are placed every 500 ft (152.4 m) along the mainline traffic lanes to aid in determining the lot and sublot limits.
The definitions of lot, sublot, and sampling frequency for thickness, concrete strength, and initial PI are presented below.
Lot Definition
 Each lot is one paving pass in width. This width can be equal to one, two, or more traffic lanes (see below for consideration of concrete shoulders).
 A lot consists of a minimum of three sublots that are each 500 ft (152.4 m) in length, and they all exist consecutively (longitudinally) along the same paving width. A lot cannot be divided between two adjacent or separated paving lanes.
 Therefore, the minimum length of a lot is 1,500 ft (457.2 m) along the same paving lane(s), and this lot can include work from 1 or more days of paving.
 The maximum lot length is defined as 1 day’s production of one paving pass, or 4,500 ft (1,371.6 m) in length, whichever is less. If the 1day production is longer than 4,500 ft (1,371.6 m), the engineer will divide the 1day production into multiple lots that meet the minimum lot length as defined above. The engineer may terminate the lot if there is any reason to believe that a special cause affected the process and resulted in a significant shift in the mean or standard deviation of thickness, PI, or strength (AQCs).
 If the contractor builds a paving pass in a given day that is less than 1,500 ft (457.2 m), this is defined as a partial lot. A partial lot is combined with the previous or next day’s paving to produce a full lot with a minimum length of 1,500 ft (457.2 m) and a maximum length of 4,500 ft (1,371.6 m). If the combined length of paving of a partial lot and the current lot being paved is greater than 4,500 ft (1,371.6 m), the lot will be limited to 4,500 ft (1,371.6 m) and another partial lot identified to be added to the next day’s paving.
 If a section of paving has been designated as a partial lot but cannot be combined with the adjacent lot (e.g., a single lane of widening or tapered paving that is less than 1,500 ft (457.2 m), or if it is the last lot in the paving project and is less than 1,500 ft (457.2 m), it may be grouped with a previous lot. This will be allowed even if it results in a lot that is greater than 4,500 ft (1,371.6 m). This type of flexibility must be included to make the field management of the PRS data collection feasible and efficient.
 Concrete shoulders can be included along with adjacent paved traffic lane(s), or by themselves if paved separately. If concrete shoulders are paved with a traffic lane (a paving width includes one or more traffic lanes and a concrete shoulder), the traffic lane is tested for all AQCs (PI, strength, and thickness) but the shoulder is tested for strength and thickness only. The pay factor is computed using only the PI values obtained from the traffic lane(s). If the lot width includes only a concrete shoulder, the shoulder is tested for concrete strength and slab thickness, and PI is assumed to be at the target values of 7.0 in. (177.8 mm) mean and 1.0in. (25.4 mm) standard deviation.
Sublot Definition
 The sublot length is established at a constant 500 ft (152.4 m) so that the PI can be measured, as well as for field location expediency and consistency.
 The width of the sublot is the paving width.
 There shall be a minimum of three sublots in each lot. The maximum is nine sublots within a maximum lot size of 4,500 ft (1,371.6 m).
 If there is a sublot that is not tested for concrete strength for whatever reason, this section shall be cored as specified and tested for compressive strength at 28 days after placement. The cores shall be tested for compressive strength according to procedures required in table 8.
Table 8. Testing Procedures Used for PerformanceRelated Specification Evaluation
Acceptance Quality Characteristic 
Test Method 
Slab thickness 
AASHTO T148 
Compressive strength 
Concrete cylinders: AASHTO T23 and AASHTO T22.
Concrete cores: AASHTO T24 for sublots with missing strength data. 
Initial Profile Index 
ASTM E 1274 
Sampling Frequency Within Sublots
The sampling frequencies for slab thickness, concrete strength, and PI within a given 500ft (152.4 m) sublot are described below.
Slab Thickness: A thickness measurement for each sublot is determined by taking one core through the slab at one random location in the sublot.
Concrete Strength: The concrete strength for each sublot is determined as the average of the 28day compression tests of two replicates taken from one random batch of concrete from each sublot. Thus, the concrete strength sample size is one per sublot and the number of replicates per sample is two.
Initial Smoothness (PI): A longitudinal profile trace will be taken in each 500ft (152.4 m) length within the wheelpaths (inside and outside wheelpaths located 3 ft [0.91 m] from the edge of the slab for conventional width lanes, or 3 ft [0.91 m] from the paint stripe for widened slabs) for each traffic lane included within the sublot. The mean PI for each 500ft (152.4 m) section within the sublot will be computed. The number of replicates per pass location equals the number of wheelpaths per traffic lane. Smoothness measurement will terminate not less than 50 ft (15.2 m) from the bridge approach joint.
Existing Tennessee Pay Factor Curves
The existing TDOT pay factor curves are provided in chapter 5 and compared with the final PRS pay factor curves. The main difference in the curves is that there are no incentives available with the existing TDOT pay factor curves, only disincentives.
Development of Pay Factor Curves Using PaveSpec 3.0
A PRS recognizes that higher quality products have additional value; and, the PRS provides payment adjustment for this higher quality up to a maximum value. A PRS also recognizes that marginal quality products have reduced value and advocates payment reduction instead of requiring complete removal, unless the pavement is so deficient that replacement or corrective action is warranted.
Individual Pay Adjustment Factors
Individual pay adjustment factors for slab thickness, comprehensive strength, and initial PI shall be determined using the pay factor curves shown in figures 2 through 4 or tables 9 through 11. These curves and tables were developed using the PaveSpec 3.0 software and account for the mean and standard deviation of the AQCs for the subject pavement project. Linear interpolation or extrapolation shall be used between the values shown in these tables, if needed.
Figure 2 and table 9 show that as strength increases within the specified limits, the pay factor increases due to greater resistance to fatigue cracking from repeated truck loadings, resulting in fewer cracked slabs and lower rehabilitation costs. Also, the lower the variability (as indicated by standard deviation) of strength, the higher the pay factor. This is caused by fewer slabs containing lowstrength concrete.
Figure 2. Pay adjustment curve for 28day compressive strength of concrete.

Table 9. Compressive Strength Pay Adjustment Table (PF, %)
Lot Mean,
lbf/in^{2}** 
Lot Standard Deviation
(computed using means of 2 tests) 
0 lbf/in^{2} 
500 lbf/in^{2}* 
1,000 lbf/in^{2} 
3,000 
92.17 
91.28 
87.92 
3,250 
93.68 
92.89 
90.22 
3,500 
95.14 
94.43 
92.36 
3,750 
96.54 
95.91 
94.33 
4,000 
97.88 
97.32 
96.13 
4,250 
99.17 
98.67 
97.76 
4,500* 
100.41 
100.00 
99.23 
4,750 
101.58 
101.18 
100.52 
5,000 
102.71 
102.33 
101.65 
5,250 
103.78 
103.42 
102.62 
5,500 
104.79 
104.45 
103.41 
1 lbf/in^{2} = 6.89 kPa
*Targets
**Pay adjustment for Lot Mean less than 3,000 lbf/in^{2} are as follows:
 <3,000 to 2,751 lbf/in^{2} = 85.00 percent
 2,750 to 2,501 lbf/in^{2} = 70.00 percent
 2,500 to 2,251 lbf/in^{2} = 50.00 percent
 2,250 to 2,000 lbf/in^{2} = 25.00 percent

Figure 3 and table 10 show that as slab thickness increases within the specified limits, the pay factor increases. This is due to greater resistance to fatigue cracking from repeated truck loadings, resulting in fewer cracked slabs and lower rehabilitation costs. Also, the lower the variability (as indicated by standard deviation) of thickness, the higher is the pay factor. This results from having fewer thin slabs. One very interesting item to note from figure 3 is that as the slab thickness decreases from 13 in. (330.2 mm), the loss in pay factor is not very significant within the range shown because of the very conservative thickness design used (13 in. [330.2 mm], as determined by AASHTO at high level of reliability). The slab cracking model in PRS is predicting that a reduced slab thickness to, say, 12 in. (304.8 mm) is not showing a drastic reduction in performance. For thinner pavement designs (e.g., 9 to 11 in. [228.6 to 279.4 mm]), this dropoff would be much more dramatic.
Figure 3. Slab thickness pay adjustment curve.

Table 10. Slab Thickness Pay Adjustment Table (PF, %)
Lot Mean Slab Thickness, in. 
Lot Standard Deviation
(computed from independent cores), in) 
0 
0.5in.* 
1.0in. 
12.0 
94.26 
92.14 
90.19 
12.25 
96.24 
94.62 
93.16 
12.5 
97.94 
96.74 
95.69 
12.75 
99.35 
98.51 
97.78 
13.00* 
100.47 
100.00 
99.43 
13.25 
101.31 
100.97 
100.64 
13.50 
101.86 
101.67 
101.41 
13.75 
102.12 
102.02 
101.75 
14.00 
102.11 
102.01 
101.64 
1 in. = 25.4 mm
*Targets 
Figure 4 and table 11 show that as initial PI decreases within the specified limits, the pay factor increases. This is due to longer pavement life from better initial smoothness (smoother pavements last longer). Also, lower variability (as indicated by standard deviation) of the PI results in a higher pay factor. The cause is that fewer sublots are reaching a terminal PI level and there are lower rehabilitation costs.
Figure 4. Initial profile index pay adjustment curve.

Table 11. Initial Profile Index Pay Adjustment Table (PF, %)
Lot Mean
Profile Index (PI), in./mi** 
Lot Standard Deviation
(computed using means of 2 wheelpaths, PIs per lane), in./mi 
0 
1.0 in./mi* 
3.00 in./mi 
0 
107.29 
107.02 
106.26 
1 
106.39 
106.20 
105.60 
2 
105.44 
105.32 
104.86 
3 
104.44 
104.38 
104.04 
4 
103.39 
103.38 
103.15 
5 
102.30 
102.33 
102.18 
6 
101.16 
101.21 
101.13 
7* 
99.97 
100.00 
100.00 
8 
98.73 
98.79 
98.80 
9 
97.45 
97.50 
97.52 
10 
96.12 
96.14 
96.17 
11 
94.74 
94.72 
94.73 
12 
93.32 
93.25 
93.22 
1 in./mi = 16 mm/km
*Targets
**Measured prior to any grinding.
***If PI is > 9 in./mi, grinding is required. The PF is determined for the PI prior to grinding for > 9 to 12 in./mi. If PI > 12in./mi, the pay factor for 12 is used. 
Computation of AQC Mean and Standard Deviation
The determination of individual pay factors from figures 2 through 4 or tables 9 through 11 requires computing the mean and standard deviation of the slab thickness, compressive strength, and initial PI for the asconstructed lot based on the field testing results. These statistics are calculated as follows.
(2)
Where:
 = Mean of n random samples of the AQC under consideration for the lot
 X_{i} = Sample measurement (for PI and strength, X_{i} is a mean of multiple replicates, and for thickness is the individual core)
 n = Sample size per lot, n for each AQC is as follows:
 Compressive strength: n = number of sublots (mean of two replicate cylinders produced from each batch in sublot)
 Thickness: n = number of sublots (one core per sublot, no replicates)
 PI: n = number of sublots multiplied by number of traffic lanes in lot (each profile test consists of measurement of a 500ft [152.4 m] continuous wheelpath section, mean of two replicates [the two wheelpaths in each lane are considered replicates])
The lot thickness standard deviation (where number of replicates = 1) is computed as follows:
(3)
The compressive strength and PI unbiased lot standard deviation (where more than one replicate per sample are used) is computed as follows.
(4)
Where:
 m = Number of replicates per sample, m, for compressive strength and PI are as follows:
 Compressive strength: m = 2 replicates (i.e., two tests per batch sublot)
 PI: m = 2 replicates per lane (i.e., two wheelpaths per lane) multiplied by number of lanes in lot.
C_{SD} = Correction factor (based on the total sample size, n) used to obtain unbiased estimates of the actual lot sample standard deviation. Appropriate C_{SD} values are determined using table 12.
Table 12. Correction Factors Used to Obtain Unbiased Estimates of the Actual Standard Deviation
Number of Samples, n 
Correction Factor, C_{SD} 
2 
0.7979 
3 
0.8862 
4 
0.9213 
5 
0.9399 
6 
0.9515 
7 
0.9594 
8 
0.9650 
9 
0.9693 
10 
0.9726 
30 
0.9915 
Updated: 02/20/2015