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

2. 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 , 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) D.H. Jensen & R.C. Wurl

3. 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

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

5. 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

6. 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

7. 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

8. 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

9. 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

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

11. 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

12. 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
|57899
|122334 |9
|002344 |5 | |9
9/17/2018
IENG 486: Statistical Quality & Process Control
(c) D.H. Jensen & R.C. Wurl

13. 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) D.H. Jensen & R.C. Wurl

14. 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

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