IENG 486: Statistical Quality & Process Control IENG 486 Lecture 04 Describing Variation & Distributions 9/17/2018 IENG 486: Statistical Quality & Process Control (c) 2002-2005 D.H. Jensen & R.C. Wurl

IENG 486: Statistical Quality & Process Control 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 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.) 9/17/2018 IENG 486: Statistical Quality & Process Control (c) 2002-2005 D.H. Jensen & R.C. Wurl

IENG 486: Statistical Quality & Process Control 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. 9/17/2018 IENG 486: Statistical Quality & Process Control

Understanding Process Variation Three Aspects: Location Spread Shape Basic Statistics: Quantify Communicate 9/17/2018 IENG 486: Statistical Quality & Process Control

IENG 486: Statistical Quality & Process Control 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) 9/17/2018 IENG 486: Statistical Quality & Process Control

IENG 486: Statistical Quality & Process Control 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 9/17/2018 IENG 486: Statistical Quality & Process Control

IENG 486: Statistical Quality & Process Control 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 15.0 Mean is influenced by outliers 9/17/2018 IENG 486: Statistical Quality & Process Control

IENG 486: Statistical Quality & Process Control 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 9/17/2018 IENG 486: Statistical Quality & Process Control

IENG 486: Statistical Quality & Process Control 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! 9/17/2018 IENG 486: Statistical Quality & Process Control

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! 9/17/2018 IENG 486: Statistical Quality & Process Control

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).  +2 -2 +3 -3 + -   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 9/17/2018 IENG 486: Statistical Quality & Process Control

Shape: Stem-and-Leaf Plot IENG 486: Statistical Quality & Process Control Shape: Stem-and-Leaf Plot 48 53 49 52 51 63 60 64 59 54 47 45 79 65 62 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 9/17/2018 IENG 486: Statistical Quality & Process Control (c) 2002-2005 D.H. Jensen & R.C. Wurl

Shape: Box (and Whisker) Plot IENG 486: Statistical Quality & Process Control Shape: Box (and Whisker) Plot Max value Third quartile Mean Median First quartile Visual display of central tendency, variability, symmetry, outliers Min value 9/17/2018 IENG 486: Statistical Quality & Process Control (c) 2002-2005 D.H. Jensen & R.C. Wurl

IENG 486: Statistical Quality & Process Control 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. 9/17/2018 IENG 486: Statistical Quality & Process Control

Goals of Statistical Quality Improvement Find special causes Head off shifts in process Obtain predictable output Continually improve the process Statistical Quality Control and Improvement Improving Process Capability and Performance 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 9/17/2018 IENG 486: Statistical Quality & Process Control