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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

Material Variability…

… or

“how do we know what we have?”

types of variance
Types of Variance
  • Material
  • Sampling
  • Testing

Cumulative

Errors vs. Blunders

precision and accuracy
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
Accuracy vs. Precision

Bias

Precision

without

Accuracy

Accuracy

without

Precision

Precision

and

Accuracy

repeatibility vs reproducibility
Repeatibility vs. Reproducibility
  • Repeatability
    • Within laboratory
  • Reproducibility
    • Between laboratory
    • Bias
sampling
Sampling
  • Representativerandom samples are used to estimate the properties of the entire lot or population.
  • These samples must be subjected to statistical analysis
sampling stratified random sampling
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
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
Basic Statistics

Arithmetic Mean

“average”

Standard Deviation

“spread”

basic statistics11
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
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 vs. Lot and Sublot
  • Population - all that exists
  • Lot – unit of material produced by same means and materials
  • Sublot – partition within a lot
normal distribution
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
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

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)

Control Charts
control charts x bar chart for example
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
Use of Control Charts

Data has shifted

Data is spreading

Refer to the text for other examples of trends

example
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

control charts20
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 example21
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 charts22
Use of Control Charts

Data has shifted

Data is spreading

Refer to the text for other examples of trends

other useful statistics in ce
Other Useful Statistics in CE
  • Regression analysis
  • Hypothesis testing
  • Etc.
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