Block 22 basic concepts
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This document discusses basic concepts of statistics as they relate to quality control and quality assurance in construction. It explains that variability is inherent in all materials and processes, but can be controlled. Sources of variability include sampling, testing, materials, and construction methods. The goal of quality control/quality assurance is to reduce variability as much as possible by addressing these sources. Key statistical terms discussed include mean, median, range, variance, precision, accuracy, and bias. Frequency histograms are presented as a tool to visualize variability in data.
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Block 22 basic concepts
- 1. Senior/Graduate HMA Course Quality Control / Quality Assurance Basic Concepts of Statistics Construction QC QA Statistics 1
- 2. Total Variability • Variability – Everything varies • Variability can be controlled, but cannot be eliminated. Each material and process has some inherent variability • Assignable variability can be eliminated IF we identify the cause Construction QC QA Statistics 2
- 3. Causes of variability • Sampling • Testing • Material • Construction (production and placement) Construction QC QA Statistics 3
- 4. QC/QA and Variability Variability = variability + variability + variability (QC/QA) (sampling) (test method) (mat./const.) S2QC/QA = S2s + S2t + S2m/c Construction QC QA Statistics 4
- 5. Ideal World S2QC/QA = S2s + S2t + S2m/c S2QC/QA = S2m/c Construction QC QA Statistics 5
- 6. Sampling & testing variability • Sampling variability is caused by random variation in sampling methods or procedures • Testing variability is the result of random variation in testing performance and equipment Sampling + testing variability = about 50% of the variation in test results Construction QC QA Statistics 6
- 7. Material and construction variability • Material variability is due to the random variation that naturally exists in a given material. • Construction variability is the result of variation that is inherent in the production and construction methods. Nature avoids absolutes – variation is the rule. Construction QC QA Statistics 7
- 8. Scientific Tools to Use in the Treatment and Analysis of Variability • Statistics • Random sampling Construction QC QA Statistics 8
- 9. Population Construction QC QA Statistics 9
- 10. Sample from the Population or Lot Sample #1 Sample #2 From each sample - extraction Sample #3 - gradation - volumetrics Sample #4 Construction QC QA Statistics 10
- 11. Precision and Accuracy Precision - Variability of Repeat Measurements Accuracy - Conformity to the True Value Bias - Deviation From True Value Construction QC QA Statistics 11
- 12. Exactness of Measurement Bias Good Precision Poor Accuracy (Biased) (Average off Center) Construction QC QA Statistics 12
- 13. Exactness of Measurement Poor Precision Good Accuracy (Unbiased) (Average on Center) Construction QC QA Statistics 13
- 14. Definitions used in HMA QC/QA • Mean • Median • Range • Variance Construction QC QA Statistics 14
- 15. Mean The total value (sum) of data values divided by the number of data points (n) 50% of the value of all X1 of the data points is below S xn/2 +X2 +X3 Mean value S xn/n (average) +Xn-2 +Xn-1 S xn/2 50% of the value of all of the data points is above +Xn Construction QC QA Statistics 15
- 16. Median Center Smallest Value X1 50% of the count of X2 data points are below X3 Median value Xn-2 50% of the count of Xn-1 data points are above Largest Value Xn Construction QC QA Statistics 16
- 17. Range, R R = Max. X - Min. X Smallest Largest Spread Construction QC QA Statistics 17
- 19. Frequency Histogram Frequency 10 8 8 6 6 5 4 4 3 2 2 1 1 0 0 2 3 4 5 6 Compacted Air Voids, %
- 20. Frequency Histogram Frequency Center 10 8 8 6 6 5 4 4 3 2 2 1 1 0 0 2 3 4 5 6 Spread
- 21. 60 Asphalt Binder Contents Frequency 16 14 12 10 8 6 4 2 0 4.3 % 4.5 % 4.7 % 4.9 % 5.1 % Construction QC QA Statistics 21
- 22. 186 Pavement depths Frequency 35 30 25 20 15 10 5 0 9.0 9.5 10.0 10.5 11.0 Construction QC QA Statistics 22
- 23. Questions? Construction QC QA Statistics 23
Notas do Editor
- It is important to understand that the Total Variability of a particular material is a sum of several definable variables. These are sampling, testing, production, and actual material variability. What is important is actual material variability. Variation of construction materials is inevitable and unavoidable. If you can assign the variability to a specific cause – such as segregation of the mix or a problem with a cold feed belt it should be fixed and eliminated.
- Everything varies. In HMA construction the sources of the variability is listed on this slide. The goal is to reduce the variability resulting from sampling and testing so that the test results are related to the process being sampled and tested.
- In construction we want to minimize variability. Variability in your test results is a combination of the variability caused by sampling, the test procedure and the material and construction process used. Sampling variability is caused by the random variation in the sampling methods and procedures. Even when everything is done right there will be some variation caused by the sampling process. Testing variability is caused by the random variation in the testing methods and procedures. Even when everything is done right there will be some variation caused by the testing process. Sampling and testing variability can cause up to 50% of the overall variation in the test results. Therefore, it is very important that the sampling and testing personnel be properly trained and that it is emphasized to them that they must follow the established procedures. There is some natural variation in the variability in materials and construction. But, it can also be controlled by using consistent construction practices and procedures.
- The goal is to have the only source of variability to be that associated with the materials and construction process.
- Sampling variability is caused by random variation that is naturally inherent
- The key to understanding variability is the use statistical analysis procedures along with statistical sampling (random sampling) procedures. Statistics is the science that deals with the treatment and analysis of numerical data. Random sampling is a sampling procedure where any specimen in the population has an equal chance of being sampled.
- A population consists of all possible observations of a particular type. A sample A large cube-shaped object can be thought of as a 100 tons of Hot Mix Asphalt. The 100 tons consists of smaller cube-shaped blocks which represent potential specimens. Assume that the cube represents a lot of hot mix and that we wish to know the density of the hot mix in the lot. Obviously, to determine the “best” estimate of the density, every bit of material in the lot must be tested (complete enumeration). Since complete enumeration is not feasible, sampling is the practical solution.
- A sample can be selected from the lot of material, and data from the sample can be used to estimate the density of the hot mix in the lot in order to make a decision regarding its acceptability. The relationship between the properties of the sample and the properties of the population is an important aspect of statistical theory and practice since “good” estimates of the properties of a population require valid samples. Two concepts that are of particular importance for ensuring sample validity are random sampling and controlled conditions.
- Another concept of importance to the analysis of construction data is the concept of precision and accuracy. It is desirable to have both precision and accuracy in your test results. The concepts of Precision and Accuracy are fundamental to the understanding of variability. 1. Precision refers to the variability of repeat measurements under carefully controlled conditions. 2. Accuracy is the conformity of results to the true value (absence of bias). 3. Bias is a tendency of an estimate to deviate in one direction from the true value.
- The analogy of a target is a practical way of understanding the relationship between precision and accuracy. A practical difficulty in measuring accuracy is that the true value must be determined. Ideally, the true value should be determined/measured by a method of high precision and with as little bias as possible. Example: Good precision but poor accuracy (biased).
- Example: Poor precision, but good accuracy (unbiased).
- There are a number of terms used in statistics. These are the common terms used in QC/QA for hot mix asphalt.
- A measure of the center of data is called the mean. The mean is the average value of all the data.
- Another measure of the center of data is called the median. The median is the value for which half the data are smaller and half the data are larger. One advantage of the median is that it is not affected by extreme values (sometimes called outliers) as the mean may be.
- Another term used to evaluate construction data is the range. It is the highest value minus the lowest value.
- 19 Training Module III - QC/QA Concepts In statistical analysis procedures, the symmetrical grouping of data around the mean (or average) is defined as the normal distribution. The normal probability distribution is completely described if the average (mean) and the variation of the data (standard deviation) are known. The normal distribution curve is bell-shaped with a single peak at the center and tails out symmetrically on each end. There is not a single normal distribution curve, but a family of distributions with the same shape or mathematical form. We use two terms to describe the normal distribution curve: the mean or average and the standard deviation.
- 17 Training Module III - QC/QA Concepts A common way of showing construction data is a histogram. In a histogram the intervals are selected for grouping the data are shown on the horizontal axis and the frequencies of occurrence with the selected intervals are plotted on the vertical axis. By maintaining intervals of equal length, all results represent equal values of area, and the total area represents the sum of all results. The histogram shown here is for air content from a paving project. It is typical of the shape of histograms that are seen in many highway materials and construction. The Frequency Histogram is a graphical representation of the occurrence of observations for a range of specific values of a selected parameter.
- 17 Training Module III - QC/QA Concepts A histogram is a particularly informative way of presenting data because it can be used to estimate quickly the center, extremes and the spread (dispersion) of the data.
- Another example of a histogram. In this histogram 60 asphalt binder contents where taken from one HMA. They are centered about 4.7 % and range from 4.3% to 5.1%.
- This is an example of a histogram. It shows that the depth of 186 pavement cores will peak in the middle and tail out on both ends.