INDE 2333ENGINEERING STATISTICS I

LECTURE 1

University of HoustonDept. of Industrial Engineering

Houston, TX 77204-4812(713) 743-4195

AGENDA

Some statistics related quotes Importance of Probability and Statistics Basic Concepts Treatment of data

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

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

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

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

VODKA, KETCHUP, ETC

ml

observations

101010021000FDA

TREATMENT OF DATA

General Concepts Pareto and Dot Diagrams Frequency Distributions Graphs of Frequency Distributions Descriptive Measures Quartiles and Percentiles X bar and s

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

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

PARETO CHARTGasket Ring

NumberOf Obs

Hole TooSmall

Hole TooLarge

Chipped Scratched AllOthers

PARETO CHARTGasket Ring

Cost ofDefects

HoleTooSmall

HoleTooLarge

Chipped Scratched AllOthers

DOT DIAGRAMS

Visually summarizes individual data Check for unusual patterns Easily identifies outliers Differences in data sources

Machines Personnel Materials

DOT DIAGRAMS

0-5 5

Deviation from nominal value in um

Day Shift Night Shift

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

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

CUMULATIVE DISTRIBUTION

Total number of observations less than a given value

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

GRAPHS OF FREQUENCY DISTRIBUTIONS

Histogram of cell observations Horizontal or vertical Size is based on observations in each cell

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)

OGIVE

Graph of cumulative distribution

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

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

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

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

DESCRIPTIVE MEASURES

Mean Median Mode Minimum Maximum Range Variance Standard Deviation Coefficient of variation

MEAN

X bar Arithmetic average of all values Sum of all values divided by number of values Sample mean and population mean

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

MODE

Most common value

MINIMUM

Smallest value

MAXIMUM

Largest value

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

RANGE

= Maximum value – minimum value

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

SAMPLE VARIANCE

1

1

2

2

n

xxs

n

ii

SAMPLE STANDARD DEVIATION

Absolute measure of dispersion Based on square root of variance

SAMPLE STANDARD DEVIATION

1

1

2

n

xxs

n

ii

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

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

BOX PLOT

Minimum Maximum

Median

Q1 Q2