Chapter 11
Statistical
Thinking and
Applications
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Key Idea
Raw data collected from the field do not
provide the information necessary for
quality control or improvement. Data must
be organized, analyzed, and interpreted.
Statistics provide an efficient and effective
way of obtaining meaningful information
from data, allowing managers and workers
to control and improve processes.
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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
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Sources of Variation in
Production Processes
Operators
Materials
INPUTS
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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Key Idea
A system governed only by common
causes is called a stable system.
Understanding a stable system and the
differences between special and common
causes of variation is essential for
managing any system.
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Problems Created by Variation
 Variation
increases unpredictability.
 Variation reduces capacity utilization.
 Variation contributes to a “bullwhip” effect.
 Variation makes it difficult to find root
causes.
 Variation makes it difficult to detect
potential problems early.
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Importance of Understanding
Variation
time
PREDICTABLE
?
UNPREDECTIBLE
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Two Fundamental
Management Mistakes
1.
2.
Treating as a special cause any fault,
complaint, mistake, breakdown, accident or
shortage when it actually is due to common
causes
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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Deming’s Red Bead Experiment
Dr. Deming used his “red bead” experiment to demonstrate that
the success or failure of workers is primarily a function of the
system they work in, and not their loyalty and effort.
Given a container of 20 red balls and 80 white balls, the worker
is asked to select only white balls. When a red ball is selected,
the worker is criticized. When a white ball is selected, the
worker is praised. Goal setting is then attempted to motivate
the workers. Inspectors are employed to audit the process.
•
•
•
•
Questions:
How does this process affect worker morale, productivity and
quality?
What should be done to improve the outcome?
How would goal setting improve this process?
How do external inspectors help?
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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 Foundations
 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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Key Idea
A good sampling plan should select a
sample at the lowest cost that will provide
the best possible representation of the
population, consistent with the objectives
of precision and reliability that have been
determined for the study.
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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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Statistical Methods
 Descriptive
statistics
 Statistical inference
 Predictive statistics
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Key Idea
One of the biggest mistakes that people
make in using statistical methods is
confusing data that are sampled from a
static population (cross-sectional data)
with data sampled from a dynamic
process (time series data).
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Enumerative and Analytic
Studies
 Enumerative
study – analysis of a static
population
study – analysis of a dynamic
time series
 Analytic
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Design of Experiments
 A designed
experiment is a test or series
of tests that enables the experimenter to
compare two or more methods to
determine which is better, or determine
levels of controllable factors to optimize
the yield of a process or minimize the
variability of a response variable.
 DOE is an increasingly important tool for
Six Sigma.
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