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- 1. Senior/Graduate HMA Course Quality Control / Quality Assurance Basic Concepts of StatisticsConstruction QC QA Statistics 1
- 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 causeConstruction QC QA Statistics 2
- 3. Causes of variability• Sampling• Testing• Material• Construction (production and placement)Construction QC QA Statistics 3
- 4. QC/QA and VariabilityVariability = variability + variability + variability(QC/QA) (sampling) (test method) (mat./const.) S2QC/QA = S2s + S2t + S2m/c Construction QC QA Statistics 4
- 5. Ideal World S2QC/QA = S2s + S2t + S2m/c S2QC/QA = S2m/cConstruction QC QA Statistics 5
- 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 resultsConstruction QC QA Statistics 6
- 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 7
- 8. Scientific Tools to Use in the Treatment and Analysis of Variability• Statistics• Random samplingConstruction QC QA Statistics 8
- 9. PopulationConstruction QC QA Statistics 9
- 10. Sample from the Population or Lot Sample #1 Sample #2 From each sample - extractionSample #3 - gradation - volumetrics Sample #4Construction QC QA Statistics 10
- 11. Precision and Accuracy Precision - Variability of Repeat Measurements Accuracy - Conformity to the True Value Bias - Deviation From True ValueConstruction QC QA Statistics 11
- 12. Exactness of Measurement Bias Good Precision Poor Accuracy (Biased)(Average off Center) Construction QC QA Statistics 12
- 13. Exactness of Measurement Poor Precision Good Accuracy (Unbiased)(Average on Center) Construction QC QA Statistics 13
- 14. Definitions used in HMA QC/QA • Mean • Median • Range • VarianceConstruction QC QA Statistics 14
- 15. Mean The total value (sum) of data values divided by the number of data points (n) 50% of the value of all X1 of the data points is below S xn/2+X2+X3 Mean value S xn/n (average)+Xn-2+Xn-1 S xn/2 50% of the value of all of the data points is above+XnConstruction QC QA Statistics 15
- 16. Median CenterSmallest Value X1 50% of the count of X2 data points are below X3 Median value Xn-2 50% of the count of Xn-1 data points are aboveLargest Value Xn Construction QC QA Statistics 16
- 17. Range, R R = Max. X - Min. XSmallest Largest SpreadConstruction QC QA Statistics 17
- 18. NormalDistribution
- 19. Frequency HistogramFrequency10 8 8 6 6 5 4 4 3 2 2 1 1 0 0 2 3 4 5 6 Compacted Air Voids, %
- 20. Frequency HistogramFrequency Center10 8 8 6 6 5 4 4 3 2 2 1 1 0 0 2 3 4 5 6 Spread
- 21. 60 Asphalt Binder Contents Frequency 16 14 12 10 8 6 4 2 0 4.3 % 4.5 % 4.7 % 4.9 % 5.1 %Construction QC QA Statistics 21
- 22. 186 Pavement depths Frequency353025201510 5 0 9.0 9.5 10.0 10.5 11.0Construction QC QA Statistics 22
- 23. Questions?Construction QC QA Statistics 23

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