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IENG 486 Lecture 04

IENG 486 Lecture 04. Describing Variation & Distributions. Assignment: . Print off Review Data from link on Materials pg. Bring the data and your exam calculator to next class Reading: Chapter 1: (1.1, 1.3 – 1.4.5) Cursory – get Fig. 1.12., p.34; Deming Management,1.4.4 Liability

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IENG 486 Lecture 04

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  1. IENG 486 Lecture 04 Describing Variation & Distributions IENG 486: Statistical Quality & Process Control

  2. Assignment: • Print off ReviewData from link on Materials pg. • Bring the data and your exam calculator to next class • Reading: • Chapter 1: (1.1, 1.3 – 1.4.5) • Cursory – get Fig. 1.12., p.34; Deming Management,1.4.4 Liability • Chapter 2: (2.2 – 2.7) • Cursory – Define, Measure, Analyze, Improve, Control • Chapter 3: (3.1, 3.3.1, 3.4.1) • HW 1: Chapter 3 Exercises: • 1, 3, 4 – using exam calculator • 10 (use Normal Plots spreadsheet from Materials page) • 43, 46, 47 (use Exam Tables from Materials page – Normal Dist.) IENG 486: Statistical Quality & Process Control

  3. What is Quality • Many definitions: • Better performance • Better service • Better value • Whatever the customer says it is… • For SPC, quality means better: • Understanding of process variation, • Control of the variation in the process, and • Improvement in the process variation. IENG 486: Statistical Quality & Process Control

  4. Understanding Process Variation • Three Aspects: • Location • Spread • Shape • Basic Statistics: • Quantify • Communicate IENG 486: Statistical Quality & Process Control

  5. Location: Mode • The mode is the value (or values) that occurs most frequently in a distribution. • To find the mode: • Sort the values into order (with no repeats), • Tally up how many times each value appears in the original distribution. • The mode (or modes) has the largest tally • Dist. 1 has two modes: 20 and 15 (four times, ea.) • Dist. 2 has one mode: 15 (appearing seven times) IENG 486: Statistical Quality & Process Control

  6. Location: Median • Half of the values will fall above and half of the values will fall below the median value. • To estimate the median: • Sort the values (keeping the duplicates in the list), and then count from one end until you get to one half (rounding down) of the total number of values. • For an odd number of values, the median is the next value. • For an even number of values, the median value is half of the sum of the current value and the next sorted value. • Dist. 1 median is 19.5 • Dist. 2 median is 15 IENG 486: Statistical Quality & Process Control

  7. Location: Mean • The mean has a special notation: x for a sample ( for the entire population) • To calculate the mean: • add up all of the values • divide the sum by the number of values • Dist. 1 mean is 18.6, • Dist. 2 mean is 15.0Mean is influenced by outliers IENG 486: Statistical Quality & Process Control

  8. Spread: Range • Range is the difference between the maximum and the minimum values, denoted R. • This value gives us the extreme limits of the distribution spread. • Much easier to calculate than other measures • Very sensitive to outliers • Range of Dist. 1 is 11 • Range of Dist. 2 is 4 IENG 486: Statistical Quality & Process Control

  9. Spread: Variance • Variance has the symbol 2 when referring to the entire population (S2 for a sample variance) • The formula for the variance is: • Measures the dispersion with less emphasis on outliers • Units for variance aren’t very intuitive • Calculation is unpleasant (calculating equation could be used) • The variance for Dist. 1 is 10.58, for Dist. 2 it is 1.63 If population is known, use n in denominator! IENG 486: Statistical Quality & Process Control

  10. Spread: Standard Deviation • The standard deviation ( for the population,or S for a sample) is the square root of the variance. • Defn. Special calculating formula: • Not as easily influenced by outliers • Has the same units as measure of location. • Std deviation for Dist. 1 is 3.25 • Std deviation for Dist. 2 is 1.28 If population is known, use n in denominator! IENG 486: Statistical Quality & Process Control

  11. -3 - + +3 -2  +2 Shape: Prob. Density Functions • The shape of a distribution is a function that maps each potential x-value to the likelihood that it would appear if we sampled at random from the distribution. This is the probability density function (PDF).  1 :68.26% of the total area  2 :95.46% of the total area  3 :99.73% of the total area Area Under the Normal Curve IENG 486: Statistical Quality & Process Control

  12. Divide each number into: Stem – one or more of the leading digits Leaf – remaining digits (may be ordered) Choose between 4 and 20 stems StatGraphics Output: Stem-and-Leaf Display 5 4|57899 6 5|122334 1 5|9 6 6|002344 1 6|5 0 7| 1 7|9 Shape: Stem-and-Leaf Plot IENG 486: Statistical Quality & Process Control

  13. Shape: Box (and Whisker) Plot • Visual display of • central tendency, variability, symmetry, outliers Max value Third quartile Mean Median First quartile Min value IENG 486: Statistical Quality & Process Control

  14. Shape: Histogram • A histogram is a vertical bar chart that takes the shape of the distribution of the data. The process for creating a histogram depends on the purpose for making the histogram. • One purpose of a histogram is to see the shape of a distribution. To do this, we would like to have as much data as possible, and use a fine resolution. • A second purpose of a histogram is to observe the frequency with which a class of problems occurs. The resolution is controlled by the number of problem classes. IENG 486: Statistical Quality & Process Control

  15. Goals of Statistical Quality Improvement Statistical Quality Control and Improvement Improving Process Capability and Performance • Find special causes • Head off shifts in process • Obtain predictable output • Continually improve the process Continually Improve the System Characterize Stable Process Capability Head Off Shifts in Location, Spread Time Identify Special Causes - Bad (Remove) Identify Special Causes - Good (Incorporate) Reduce Variability Center the Process LSL 0 USL IENG 486: Statistical Quality & Process Control

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