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Material Variability…. … or “how do we know what we have?”. Why are materials and material properties variable?. Metals Concrete Asphalt Wood Plastic. Types of Variance. Material Sampling Testing. Cumulative. Errors vs. Blunders. Precision and Accuracy.
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Material Variability… … or “how do we know what we have?”
Why are materials and material properties variable? • Metals • Concrete • Asphalt • Wood • Plastic
Types of Variance • Material • Sampling • Testing Cumulative Errors vs. Blunders
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
Accuracy vs. Precision Bias Precision without Accuracy Accuracy without Precision Precision and Accuracy
Repeatibility vs. Reproducibility • Repeatability • Within laboratory • Reproducibility • Between laboratory • Bias
Sampling • Representativerandom samples are used to estimate the properties of the entire lot or population. • These samples must be subjected to statistical analysis
Day 1 Day 2 Day 3 Lot #1 Lot # 2 Lot # 2 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”
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
Basic Statistics Arithmetic Mean “average” Standard Deviation “spread”
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
Coefficient of Variation • A way to combine ‘mean’ and ‘standard deviation’ to give a more useful description of the material variability
Population vs. Lot and Sublot • Population - all that exists • Lot – unit of material produced by same means and materials • Sublot – partition within a lot
m= mean Frequency 34.1% 34.1% 2.2% 2.2% 13.6% 13.6% Normal Distribution Large spread Small spread +1s -3s -1s +2s +3s -2s
LRFD(Load and resistance factor design method)for Instance… A very small probability that the load will be greater than the resistance Resistance Load Mean resistance Mean load
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) Control Charts
Control Charts (X-bar chart for example) Moving mean of 3 consecutive tests Mean of 2nd 3 tests UCL Target Result LCL Mean of 1st 3 tests Sample Number
Use of Control Charts Data has shifted Data is spreading Refer to the text for other examples of trends
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%? Req’d mean = ?? • Solution to 1. • z ~ -3 -3s • m – 3s = 80 ksi • Required mean = 86 ksi • What does it mean? • Solution to 2. • z~ -1.2817 -1.2817s • m – 1.2817s = 80 ksi • Required mean = 82.6 ksi • What is the difference between 1 and 2 80 ksi +1s -3s -1s +2s +3s -2s
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) Control Charts
Control Charts (X-bar chart for example) Moving mean of 3 consecutive tests Mean of 2nd 3 tests UCL Target Result LCL Mean of 1st 3 tests Sample Number
Use of Control Charts Data has shifted Data is spreading Refer to the text for other examples of trends
Other Useful Statistics in CE • Regression analysis • Hypothesis testing • Etc.