Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Learning Objectives
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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3.1 Describing Variation
Stem-and-Leaf Display
Easy to find percentiles of the data; see page 69
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Plot of Data in Time Order
Marginal plot
produced by
MINITAB
Also called a run chart
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Histograms – Useful for large data sets
Group values of the variable into bins, then count the number
of observations that fall into each bin
Plot frequency (or relative frequency) versus the values of
the variable
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Additional Minitab Graphs
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Numerical Summary of Data
Sample average:
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Standard Deviation
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Box Plot
(or Box-and-Whisker Plot)
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Comparative Box Plots
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Probability Distributions
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Sometimes called a
probability mass function
Sometimes called a
probability density function
Will see many examples in the text
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The mean is the point at which the distribution exactly “balances”.
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The mean is not necessarily the 50th percentile of the distribution
(that’s the median)
The mean is not necessarily the most likely value of the random
variable (that’s the mode)
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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3.2 Important Discrete Distributions
The Hypergeometric Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Discrete distributions are used frequently in designing acceptance
sampling plans – see Chapter 15
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Binomial Distribution
Basis is in Bernoulli trials
The random variable x is the number of successes out of n
Bernoulli trials with constant probability of success p on each trial
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Binomial Distributions
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Poisson Distribution
Frequently used as a model for count data
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Negative Binomial Distribution
The random variable x is the number of Bernoulli trials upon
which the rth success occurs
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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•The negative binomial distribution is also
sometimes called the Pascal distribution
•When r = 1 the negative binomial distribution is
known as the geometric distribution
• The geometric distribution has many useful
applications in SQC
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Geometric Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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3.3 Important Continuous Distributions
The Normal Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Central Limit Theorem
Practical interpretation – the sum of independent random
variables is approximately normally distributed regardless of
the distribution of each individual random variable in the sum
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Lognormal Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Exponential Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Relationship between the Poisson and exponential distributions
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Lack-of-memory property
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Gamma Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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When r is an integer, the gamma distribution is the result of summing r
independently and identically exponential random variables each with
parameter λ.
The gamma distribution has many applications in reliability engineering.
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Weibull Distribution
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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When β = 1, the
Weibull reduces to
the exponential
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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An Application of the Weibull Distribution
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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3.4 Probability Plots
• Determining if a sample of data might reasonably be
assumed to come from a specific distribution
• Probability plots are available for various
distributions
• Easy to construct with computer software
(MINITAB)
• Subjective interpretation
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Normal Probability Plot
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Normal Probability Plot on Standard Graph Paper
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Other Probability Plots
• What is a reasonable choice as a probability model
for these data?
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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3.5 Some Useful Approximations
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Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Learning Objectives
Chapter 3
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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