Engineering Statistics

1. Engineering Statistics Kanchalasudtachat

2. Statistics • Deals with • Collection • Presentation • Analysis and use of data to make decision • Solve problems and design products and processes • Can be powerful tool for • Designing new products and systems • Improving existing design • Designing, developing and improving production processes

3. Variability

4. Collecting Engineering Data • Retrospective Study • Would be either all or a sample of the historical process data. • Observational Study • Would be either observations of process or population. • Are usually conducted for short time period. • Designed Experiments • Collect the observations of the resulting system output data.

5. Random Samples • Statistical methods work correctly and produce valid results. Random samples must be used. • Each possible sample of size n has an equally likely chance of being selected.

6. Chapter 2Data Summary and Presentation Kanchalasudtachat

7. Content • Random Sampling • Stem-And-Leaf Diagrams • Histograms • Box Plots • Time Series plots • Multivariate Data

8. Sample Statistics: x, s, p, r, etc. Population Parameters: , , r, etc. Population and Sample Probability (sampling) Inference (predict)

9. Data Summary and Display • Sample mean Population mean

10. Example 2.1

11. Sample Variance and Sample Standard Deviation Population variance

12. Stem-And-Leaf Diagrams • Stem-And-Leaf Diagrams is a good way to obtain an informative visual display of a data. • Each number consists of at least two digits. • Steps for constructing • Divide each number into two parts: a stem, and a leaf. • List the stem value in a vertical column. • Record the leaf for each observation • Write the units for stems and leaves on the display

13. Example 2-4

14. Example 2-4

15. Histograms • Use the horizontal axis to represent the measurement scale for the data. • Use The Vertical scale to represent the counts, or frequencies.

16. Example 2-6

17. Pareto Chart • This chart is widely used in quality and process improvement studies. • Data usually represent different types of defects, failure modes, or other categories. • Chart usually exhibit “Pareto’s law” Example 2-8

19. Example 2-8

20. Box Plot • Describes several features of a data set, such as center, spread, departure from symmetry, and identification of observations. • The observations are called “outliers.” • The box encloses the interquartile range (IQR) with left at the first quartile, q1, and the right at the third quartile, q3. • A line, or whisker, extends from each end of the box. • The lower whisker extends to smallest data point within 1.5 interquartile ranges from first quartile. • The upper whisker extends to largest data point within 1.5 interquartile ranges from third quartile.

21. Box Plot

22. Example • 63, 88, 89, 89, 95, 98, 99, 99, 100, 100 • A lower quartile of Q1 = 89  • An upper quartile of Q3 = 99 • Hence the box extends from 89 to 99 and the interquartile range IQR is 99 - 89 = 10. • An outlier is any data point that is more than 1.5 times the IQR from either end of the box. • 1.5 times the IQR is 1.5*10= 15 so, at the upper end an outlier is any data point more than 99+15=114. • There are no data points larger than 114, so there are no outliers at the upper end. • At the lower end an outlier is any data point less than 89 - 15 = 74. There is one data point, 63, which is less than 74 so 63 is an outlier.

23. Time Series Plots

24. Multivariate Data • The corrected sum of cross-products

25. Scatter Diagrams • Diagram is a simple descriptive tool for multivariate data. • The diagram is useful for examining the pairwise (or two variables at a time) relationships between the variables.

26. Example

27. Example: Scatter diagrams and box plots

28. Scatter diagrams • Scatter diagrams for different values of the sample correlation coefficient r

29. Questions?