block 22 basic concepts
TRANSCRIPT
Construction QC QA Statistics 1
Quality Control / Quality Assurance
Basic Concepts of Statistics
Senior/GraduateHMA Course
Construction QC QA Statistics 2
Total Variability
• Variability – Everything varies• Variability can be controlled, but cannot be
eliminated. Each material and process has some inherent variability
• Assignable variability can be eliminated IF we identify the cause
Construction QC QA Statistics 3
Causes of variability
• Sampling• Testing• Material• Construction (production and placement)
Construction QC QA Statistics 4
QC/QA and Variability
Variability = variability + variability + variability
(QC/QA) (sampling) (test method) (mat./const.)
S2QC/QA = S2
s + S2t + S2
m/c
Construction QC QA Statistics 5
Ideal World
S2QC/QA = S2
s + S2t + S2
m/c
S2QC/QA = S2
m/c
Construction QC QA Statistics 6
Sampling & testing variability
• Sampling variability is caused by random variation in sampling methods or procedures
• Testing variability is the result of random variation in testing performance and equipment
Sampling + testing variability = about 50% of the variation in
test results
Construction QC QA Statistics 7
Material and construction variability
• Material variability is due to the random variation that naturally exists in a given material.
• Construction variability is the result of variation that is inherent in the production and construction methods.
Nature avoids absolutes – variation is the rule.
Construction QC QA Statistics 8
Scientific Tools to Use in the Treatment and Analysis of Variability
• Statistics• Random sampling
Construction QC QA Statistics 9
Population
Construction QC QA Statistics 10
Sample from thePopulation or Lot
Sample #1
Sample #3
Sample #2
From each sample- extraction- gradation- volumetrics
Sample #4
Construction QC QA Statistics 11
Precision and Accuracy
Precision - Variability of Repeat Measurements
Accuracy - Conformity to the True Value
Bias - Deviation From True Value
Construction QC QA Statistics 12
Exactness of Measurement
Good PrecisionPoor Accuracy
(Biased)
(Average off Center)
Bias
Construction QC QA Statistics 13
Exactness of Measurement
Poor PrecisionGood Accuracy
(Unbiased)
(Average on Center)
Construction QC QA Statistics 14
Definitions used in HMA QC/QA
• Mean• Median• Range• Variance
Construction QC QA Statistics 15
MeanThe total value (sum) of data values divided
by the number of data points (n)
X1
+X2
+X3
+Xn-2
+Xn-1
+Xn
50% of the value of allof the data points is below
50% of the value of allof the data points is above
Mean value(average)
S xn/n
S xn/2
S xn/2
Construction QC QA Statistics 16
MedianCenter
X1
X2
X3
Xn-2
Xn-1
Xn
SmallestValue
LargestValue
50% of the count of data points are below
50% of the count of data points are above
Median value
Construction QC QA Statistics 17
R = Max. X - Min. X
Spread
Range, R
Smallest Largest
NormalDistribution
Frequency Histogram
Frequency
1
3
5
8
2
4
6
1
Compacted Air Voids, %
0
2
4
6
8
10
0 2 3 4 5 6
Frequency Histogram
Frequency
1
3
5
8
2
4
6
1
0
2
4
6
8
10
0 2 3 4 5 6
Center
Spread
Construction QC QA Statistics 21
60 Asphalt Binder Contents
02468
10121416
Frequency
4.3 % 5.1 %4.7 %4.5 % 4.9 %
Construction QC QA Statistics 22
0
5
10
15
20
25
30
35Frequency
186 Pavement depths
9.0 10.0 10.5 11.09.5
Construction QC QA Statistics 23
Questions?