block 22 basic concepts

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?