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INDE 2333ENGINEERING STATISTICS I
LECTURE 1
University of HoustonDept. of Industrial Engineering
Houston, TX 77204-4812(713) 743-4195
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AGENDA
Some statistics related quotes Importance of Probability and Statistics Basic Concepts Treatment of data
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SOME STATISTICS RELATED QUOTES
“Not all that can be counted counts, not all that counts can be counted”
In order to improve a process, you must first be able to measure it
Right the first time There are three types of liars:
Liars, damn liars, and statisticians
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IMPORTANCE OF PROBABILITY AND STATISTICS
Walter Shewhart, 1920’s Japan’s manufacturing rise, 1950’s U.S. Manufacturing Crisis, 1980’s
Crosby, “Quality is Free” Juran Deming, 14 points Malcolm Baldridge Award Tom Peters, Harley-Davidson
Tools Ishikawa, Pareto, and SPC Charts JIT Benchmarking 6 Sigma, Motorola
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BASIC CONCEPTS
Unit Single entity of interest Different measures
Population Set of all units of interest present
Sample Subset of the population present Measurements actually collected Samples should random not be biased
Sample size Number of units in the sample that are taken for measurement
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EXAMPLE
Sample Mean Average value of sample
Sample Standard Deviation Measurement of spread or variation in measurements
Situation Company uses automatic equipment to fill bottles FDA requires that the bottles be filled a minimum amount FDA fines company when bottles are not Automatic filling processes has inherent variation
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VODKA, KETCHUP, ETC
ml
observations
101010021000FDA
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TREATMENT OF DATA
General Concepts Pareto and Dot Diagrams Frequency Distributions Graphs of Frequency Distributions Descriptive Measures Quartiles and Percentiles X bar and s
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GENERAL CONCEPTS
Raw statistical data from surveys, experiments, etc can be too overwhelming to understand
The data must be condensed and represented in a manner that is more easily understood
Graphically Tabular or Numerical form
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PARETO DIAGRAMS
Special bar chart Based on the Pareto 80-20 Principle Ordered in descending order of interest Allows attention to be directed on most important
areas Frequently include cost related data
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PARETO CHARTGasket Ring
NumberOf Obs
Hole TooSmall
Hole TooLarge
Chipped Scratched AllOthers
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PARETO CHARTGasket Ring
Cost ofDefects
HoleTooSmall
HoleTooLarge
Chipped Scratched AllOthers
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DOT DIAGRAMS
Visually summarizes individual data Check for unusual patterns Easily identifies outliers Differences in data sources
Machines Personnel Materials
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DOT DIAGRAMS
0-5 5
Deviation from nominal value in um
Day Shift Night Shift
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FREQUENCY DISTRIBUTIONS
Table of data Divided in classes / categories / cells Number of cells is usually related to the total obs Class / category / cell limits Class / category / cell frequencies
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FREQUENCY DISTRIBUTIONS
Class Limits Frequency
5.0-8.9 3
9.0-12.9 10
13.0-16.9 14
17.0-20.9 25
21.0-24.9 17
25.0-28.9 9
29.0-32.9 2
Total 80
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CUMULATIVE DISTRIBUTION
Total number of observations less than a given value
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CUMULATIVE DISTRIBUTION
Class Limits Cumulative Frequency
Less than 5.0 0
9.0 3
13.0 13
17.0 27
21.0 52
25.0 69
29.0 78
33.0 80
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GRAPHS OF FREQUENCY DISTRIBUTIONS
Histogram of cell observations Horizontal or vertical Size is based on observations in each cell
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GRAPHS OF FREQUENCY DISTRIBUTIONS
0
5
10
15
20
25
Cla
ss F
requ
ency
7 11 15 19 23 27 31
Emission of sulfer oxides (tons)
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OGIVE
Graph of cumulative distribution
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OGIVE
0
10
20
30
40
50
60
70
80
90
5 9 13 17 21 25 29 33
Emission of sulfer oxides (tons)
Cum
ulat
ive
Fre
quen
cy
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STEM AND LEAF DISPLAYS
Smaller sets of data Does not lose any information Class, as well as, actually data values Data values are listed to the right of the classes
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STEM AND LEAF DISPLAY
Class Limits
10-19 2 7 5
20-29 9 1 5 3 4 7 1 8
30-39 4 9 2 4 7
40-49 4 8 2
50-59 3
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STEM AND LEAF DISPLAY
Class Limits
1 2 7 5
2 9 1 5 3 4 7 1 8
3 4 9 2 4 7
4 4 8 2
5 3
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DESCRIPTIVE MEASURES
Mean Median Mode Minimum Maximum Range Variance Standard Deviation Coefficient of variation
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MEAN
X bar Arithmetic average of all values Sum of all values divided by number of values Sample mean and population mean
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MEDIAN
“Middle value” Observations are ordered from smallest to largest Median observation depends on number of obs Odd number of observations
(n+1)/2 For 5 observations, median is value of (5+1)/2=3rd observation
Even number of observations Median value is average of the two observations in positions n/2 and
(n+2)/2 For 6 observations, average values of 3rd and 4th observations
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MODE
Most common value
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MINIMUM
Smallest value
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MAXIMUM
Largest value
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RANGE
Method to measure the dispersion of the values Largest value minus the smallest value Can be misleading when outliers are present Does not take into account the distribution of
bunching of values Simple and fast to calculate so commonly used in
industry particularly with SPC charts
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RANGE
= Maximum value – minimum value
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SAMPLE VARIANCE
Absolute measure of dispersion When many values are away from the mean, the variance is
large When many values are close to the mean, the variance is
small Based on
Sample mean Squared difference of observations from sample mean Number of observations in sample
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SAMPLE VARIANCE
1
1
2
2
n
xxs
n
ii
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SAMPLE STANDARD DEVIATION
Absolute measure of dispersion Based on square root of variance
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SAMPLE STANDARD DEVIATION
1
1
2
n
xxs
n
ii
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QUARTILES AND PERCENTILES
Quartiles Groupings of 25% observations 1st, 2nd, 3rd, 4th quartile
Percentiles At least 100 p % are at or below value At least 100 (1-p) % are at or above value
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PROCEDURE FOR CALCULATING PERCENTILES
Order observations smallest to largest Calculate n * p Not an integer
Round up to next highest integer and find value Integer
Calculate mean of kth and (k+1)th observations
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BOX PLOT
Minimum Maximum
Median
Q1 Q2