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Material Variability…

This informative text delves into the variability of materials and properties in engineering, addressing precision, accuracy, and bias in testing methods. Topics covered include sampling, types of variance, statistical analysis, and quality control tools. The concept of variability, standard deviation, mean, and population versus sample are explored in depth. Practical examples and scenarios are provided to illustrate key concepts and calculations.

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Material Variability…

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  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 Bias Precision without Accuracy Accuracy without Precision Precision and Accuracy

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

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

  8. 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”

  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. 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

  15. 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

  16. 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

  17. 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

  18. Use of Control Charts Data has shifted Data is spreading 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%? 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

  20. 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

  21. 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

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

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

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