Chapter 9
Statistical Thinking
and Applications
THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson LearningTM
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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
THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson LearningTM
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Sources of Variation
in Production Processes
Materials
INPUTS
Operators
Measurement
Instruments
Methods
PROCESS
OUTPUTS
Tools
Machines
Environment
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Human
Inspection
Performance
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Variation
• Many sources of uncontrollable variation
exist (common causes)
• Special (assignable) causes of variation
can be recognized and controlled
• Failure to understand these differences
can increase variation in a system
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Importance of Understanding
Variation
time
PREDICTABLE
?
UNPREDECTIBLE
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Two Fundamental
Management Mistakes
1. Treating as a special cause any fault,
complaint, mistake, breakdown, accident
or shortage when it actually is due to
common causes
2. Attributing to common causes any fault,
complaint, mistake, breakdown, accident
or shortage when it actually is due to a
special cause
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Note to Instructors
• The following slides can be used to guide a
class demonstration and discussion of the
Deming Red Bead experiment using small
bags of M&M’s® Chocolate Candies, from
a suggestion I found on a TQ newsgroup
several years ago. The good output (“red
beads”) are the blue M&Ms, with the
instructor playing the role of Dr. Deming.
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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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Production Setup
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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Production Process
1. Production worker produces 10 pieces
and places them on the napkin.
2. Each inspector, independently, counts
the blue ones, and passes to the Chief
Inspector to verify.
3. If Chief Inspector agrees, s/he tells
the recorder, who reports it to me.
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Do it right
the first
time!
Take Pride in
Your Work!
Be a Quality Worker!
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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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Statistical Methods
• Descriptive statistics
• Statistical inference
• Predictive statistics
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Review of Key Concepts
•
•
•
•
•
•
Random variables
Probability distributions
Populations and samples
Point estimates
Sampling distributions
Standard error of the mean
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Important Probability
Distributions
• Discrete
– Binomial
– Poisson
• Continuous
– Normal
– Exponential
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Central Limit Theorem
• If simple random samples of size n are
taken from any population, the
probability distribution of sample means
will be approximately normal as n
becomes large.
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Sampling Methods
•
•
•
•
•
Simple random sampling
Stratified sampling
Systematic sampling
Cluster sampling
Judgment sampling
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Sampling Error
• Sampling error (statistical error)
• Nonsampling error (systematic error)
• Factors to consider:
– Sample size
– Appropriate sample design
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Design of Experiments
• A test or series of tests to compare two or
more methods to determine which is better,
or to determine levels of controllable factors
to optimize the yield of a process or
minimize the variability of a response
variable.
• Factorial experiment
– Analysis of all combinations of factor levels to
understand main effects and interactions
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Excel Descriptive Statistics Tool
• Tools…Data Analysis… Descriptive Statistics
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THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson LearningTM
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Excel Histogram Tool
• Tools…Data Analysis…Histogram
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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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Types of Capability Studies
• Peak performance study - how a process
performs under ideal conditions
• Process characterization study - how a
process performs under actual operating
conditions
• Component variability study - relative
contribution of different sources of variation
(e.g., process factors, measurement system)
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Process Capability Study
1.
2.
3.
4.
5.
6.
7.
Choose a representative machine or process
Define the process conditions
Select a representative operator
Provide the right materials
Specify the gauging or measurement method
Record the measurements
Construct a histogram and compute descriptive
statistics: mean and standard deviation
8. Compare results with specified tolerances
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Process Capability
(a)
specification
natural variation
(c)
specification
natural variation
(b)
specification
natural variation
(d)
specification
natural variation
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Process Capability Index
Cp = UTL - LTL
6s
Cpu = UTL - m
3s
Cpl = m - LTL
3s
Cpk = min{ Cpl, Cpu }
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PROCESS_CAPABILITY.XLS
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