1. Engineering Statistics KANCHALA SUDTACHAT

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 2 Data Summary and Presentation KANCHALA SUDTACHAT

7. Content 1.Random Sampling 2.Stem-And-Leaf Diagrams 3.Histograms 4.Box Plots 5.Time Series plots 6.Multivariate Data

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

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 1.Divide each number into two parts: a stem, and a leaf. 2.List the stem value in a vertical column. 3.Record the leaf for each observation 4.Write the units for stems and leaves on the display

13. 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

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, q 1, and the right at the third quartile, q 3.  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 Q 1 = 89  An upper quartile of Q 3 = 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?