1. Material Variability… … or “how do we know what we have?”

2. Why are materials and material properties variable? Metals Concrete Asphalt Wood Plastic

3. Types of Variance Material Sampling Testing Cumulative Errors vs. Blunders

4. Precision and Accuracy Precision – “variability of repeat measurements under carefully controlled conditions” Accuracy – “conformity of results to the true value” Bias – “tendency of an estimate to deviate in one direction” Addressed in test methods and specifications in standards

5. Accuracy vs. Precision Precision without Accuracy without Precision and Accuracy Bias

6. Repeatibility vs. Reproducibility Repeatability Within laboratory Reproducibility Between laboratory Bias

7. Sampling Representative random samples are used to estimate the properties of the entire lot or population. These samples must be subjected to statistical analysis

8. Sampling - Stratified Random Sampling Need concept of random samples Example of highway paving Consider each day of production as sublot Randomly assign sample points in pavement Use random number table to assign positions Each sample must have an equal chance of being selected, “representive sample” Day 1Day 2Day 3 Lot #1Lot # 2

9. Parameters of variability Average value Central tendency or mean Measures of variability Called dispersion Range - highest minus lowest Standard deviation, s Coefficient of variation, CV% (100%) (s) / Mean Population vs. sample

10. Basic Statistics Arithmetic Mean “average” Standard Deviation “spread”

11. Basic Statistics Need both average and mean to properly quantify material variability For example: mean = 40,000 psi and st dev = 300 vs. mean = 1,200 psi and st. dev. = 300 psi

12. Coefficient of Variation A way to combine ‘mean’ and ‘standard deviation’ to give a more useful description of the material variability

13. Population vs. Lot and Sublot Population - all that exists Lot – unit of material produced by same means and materials Sublot – partition within a lot

14. Normal Distribution Frequency 34.1% 13.6% 2.2%  = mean -3  -2  -1  +1  +2  +3  Small spread Large spread

15. LRFD (Load and resistance factor design method) for Instance… Load Resistance A very small probability that the load will be greater than the resistance Mean load Mean resistance

16. Control Charts Quality control tools Variability documentation Efficiency Troubleshooting aids Types of control charts Single tests X-bar chart (Moving means of several tests) R chart (Moving ranges of several tests)

17. Control Charts (X-bar chart for example) Moving mean of 3 consecutive tests Sample Number Result Mean of 1 st 3 tests Mean of 2 nd 3 tests Target UCL LCL

18. Use of Control Charts Data is spreading Data has shifted Refer to the text for other examples of trends

19. Example A structure requires steel bolts with a strength of 80 ksi. The standard deviation for the manufacturer’s production is 2 ksi. A statistically sound set of representative random samples will be drawn from the lot and tested. What must the average value of the production be to ensure that no more than 0.13% of the samples are below 80 ksi? What about no more than 10%? -3  -2  -1  +1  +2  +3  1.Solution to 1. 1.z ~ -3  -3   – 3  ksi 3.Required mean = 86 ksi 4.What does it mean? 2.Solution to 2. 1.z~ -1.2817  -1.2817   – 1.2817  = 80 ksi 3.Required mean = 82.6 ksi 4.What is the difference between 1 and 2 Req’d mean = ?? 80 ksi

20. Control Charts Quality control tools Variability documentation Efficiency Troubleshooting aids Types of control charts Single tests X-bar chart (Moving means of several tests) R chart (Moving ranges of several tests)

21. Control Charts (X-bar chart for example) Moving mean of 3 consecutive tests Sample Number Result Mean of 1 st 3 tests Mean of 2 nd 3 tests Target UCL LCL

22. Use of Control Charts Data is spreading Data has shifted Refer to the text for other examples of trends

23. Other Useful Statistics in CE Regression analysis Hypothesis testing Etc.