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## PowerPoint Slideshow about 'Material Variability…' - aizza

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Why are materials and material properties variable?

- Metals
- Concrete
- Asphalt
- Wood
- Plastic

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

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

- 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 DistributionLarge 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 ChartsControl 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 ChartsControl 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.

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