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Page 1Prof. Rushen Chahal
Prof. Rushen ChahalProf. Rushen Chahal
Statistical Thinking
and Applications
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Page 2Prof. Rushen Chahal
Statistical Thinking
All work occurs in a system of
interconnected processes
Variation exists in all processes Understanding and reducing variation
are the keys to success
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Page 3Prof. Rushen Chahal
Sources of Variation
in Production Processes
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Materials
Tools
Operators MethodsMeasurement
Instruments
HumanInspection
Performance
EnvironmentMachines
INPUTS PROCESS OUTPUTS
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Page 4Prof. Rushen Chahal
Variation
Many sources of uncontrollable
variation exist (common causes)
Special (assignable) causes of variation can be recognized and
controlled
Failure to understand thesedifferences can increase variation in
a system
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Page 5Prof. Rushen Chahal
Importance of Understanding
Variation
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time
PREDICTABLE
? UNPREDECTIBLE
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Page 6Prof. Rushen Chahal
Two Fundamental
Management Mistakes1. Treating as a special cause any fault,
complaint, mistake, breakdown, accident
or shortage when it actually is due tocommon causes
2. Attributing to common causes any fault,
complaint, mistake, breakdown, accident
or shortage when it actually is due to aspecial cause
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Page 7Prof. Rushen Chahal
Note to Instructors
The following slides can be used to guide
a class demonstration and discussion of
the Deming Red Bead experiment usingsmall bags of M&M¶s® Chocolate Candies,
from a suggestion I found on a TQ
newsgroup several years ago. The good
output (³red beads´) are the blue M&Ms,with the instructor playing the role of Dr.
Deming.
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Page 8Prof. Rushen Chahal 8
We¶re Going into Business!!!
We have a new global customer and have to start
up several factories. So I need teams of 5 to do
the work:
1 production worker
2 inspectors
1 Chief Inspector 1 Recorder
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Page 9Prof. Rushen Chahal
Production Setup
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1. Take the bag in your left hand.
2. Tear a 3/4´ opening in the right corner.(only large enough for one piece at a
time)
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Page 10Prof. Rushen Chahal
Production Process
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1. Production worker produces 10 pieces
and places them on the napkin.
2. Each inspector, independently, countsthe blue ones, and passes to the Chief
Inspector to verify.
3. If Chief Inspector agrees, s/he tellsthe recorder, who reports it to me.
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Page 11Prof. Rushen Chahal 11
Do it right
the first
time!
Be a Quality Worker!
Take Pride in
Your Work!
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Page 12Prof. Rushen Chahal
Lessons Learned
Quality is made at the top.
Rigid procedures are not enough.
People are not always the main source
of variability.
Numerical goals are often meaningless.
Inspection is expensive and does not
improve quality.
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Page 13Prof. Rushen Chahal
Statistical Methods
Descriptive statistics
Statistical inference
Predictive statistics
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Page 14Prof. Rushen Chahal
Review of Key Concepts
Random variables
Probability distributions
Populations and samples
Point estimates
Sampling distributions Standard error of the mean
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Page 15Prof. Rushen Chahal
Important Probability
Distributions Discrete
±Binomial
±Poisson
Continuous
±Normal
±Exponential
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Page 16Prof. Rushen Chahal
Central Limit Theorem
If simple random samples of size n are
taken from any population, the
probability distribution of sample meanswill be approximately normal as n
becomes large.
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Page 17Prof. Rushen Chahal
Sampling Methods
Simple random sampling
Stratified sampling
Systematic sampling
Cluster sampling
Judgment sampling
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Page 18Prof. Rushen Chahal
Sampling Error
Sampling error (statistical error)
Nonsampling error (systematic error)
Factors to consider:
±Sample size
±Appropriate sample design
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Page 19Prof. Rushen Chahal
Design of Experiments
A test or series of tests to compare twoor more methods to determine which isbetter, or to determine levels of controllable factors to optimize the yieldof a process or minimize the variabilityof a response variable.
Factorial experiment ± Analysis of all combinations of factor levels
to understand main effects and interactions
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Page 20Prof. Rushen Chahal
Excel Descriptive Statistics
Tool Tools«Data Analysis« Descriptive Statistics
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Page 21Prof. Rushen Chahal 21
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Page 22Prof. Rushen Chahal
Excel Histogram Tool
Tools«Data Analysis«Histogram
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Page 23Prof. Rushen Chahal 23
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Page 24Prof. Rushen Chahal
Process Capability
The range over which the natural variation
of a process occurs as determined by the
system of common causes
Measured by the proportion of output that
can be produced within design
specifications
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Page 25Prof. Rushen Chahal 25
Types of Capability Studies
Peak performance study - how a process
performs under ideal conditions
Process characterization study - how a
process performs under actual operatingconditions
Component variability study - relative
contribution of different sources of variation(e.g., process factors, measurement system)
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Page 26Prof. Rushen Chahal 26
Process Capability Study
1. Choose a representative machine or process
2. Define the process conditions
3. Select a representative operator
4. Provide the right materials
5. Specify the gauging or measurement method
6. Record the measurements
7. Construct a histogram and compute descriptivestatistics: mean and standard deviation
8. Compare results with specified tolerances
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Page 27Prof. Rushen Chahal
Process Capability
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specification specification
specification specification
natural variation natural variation
(a) (b)
natural variation natural variation
(c) (d)
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Page 28Prof. Rushen Chahal
Process Capability Index
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Cp = UTL - LTL
6W
Cpl, Cpu }
UTL - Q3W
Cpl = Q - LTL
3W
Cpk = min{
Cpu =
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Page 29Prof. Rushen Chahal
PROCESS_CAPABILITY.XLS
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