chapter 31introduction to statistical quality control, 7th edition by douglas c. montgomery....
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Chapter 33Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Easy to find percentiles of the data; see page 69 Stem-and-Leaf Display 3.1 Describing VariationTRANSCRIPT
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Chapter 3 1Introduction 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 2Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 3Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Easy to find percentiles of the data; see page 69
Stem-and-Leaf Display3.1 Describing Variation
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Chapter 3 4Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Also called a run chart
Plot of Data in Time OrderMarginal plot produced by MINITAB
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Chapter 3 5Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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
Histograms – Useful for large data sets
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Chapter 3 6Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Additional Minitab Graphs
Chapter 3 7Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 8Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 9Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Numerical Summary of DataSample average:
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Chapter 3 10Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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The Standard Deviation
Chapter 3 11Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 12Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Box Plot(or Box-and-Whisker Plot)
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Chapter 3 13Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Comparative Box Plots
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Chapter 3 14Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Probability Distributions
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Chapter 3 15Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 16Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Will see many examples in the text
Sometimes called a probability mass function
Sometimes called a probability density function
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Chapter 3 17Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 18Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 19Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The mean is the point at which the distribution exactly “balances”.
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Chapter 3 20Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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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Chapter 3 21Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 22Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Hypergeometric Distribution
3.2 Important Discrete Distributions
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Chapter 3 23Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Discrete distributions are used frequently in designing acceptance sampling plans – see Chapter 15
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Chapter 3 24Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 25Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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
The Binomial Distribution
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Chapter 3 26Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Binomial Distributions
Chapter 3 27Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 28Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 29Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Frequently used as a model for count data
The Poisson Distribution
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Chapter 3 30Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 31Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 32Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The random variable x is the number of Bernoulli trials upon which the rth success occurs
The Negative Binomial Distribution
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Chapter 3 33Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
•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
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Geometric Distribution
Chapter 3 34Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 35Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Normal Distribution3.3 Important Continuous Distributions
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Chapter 3 36Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 37Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 38Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 39Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 40Introduction 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
Chapter 3 41Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Practical interpretation – the sum of independent random variables is approximately normally distributed regardless of the distribution of each individual random variable in the sum
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Chapter 3 42Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Lognormal Distribution
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Chapter 3 43Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 44Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 45Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Exponential Distribution
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Chapter 3 46Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Relationship between the Poisson and exponential distributions
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Lack-of-memory property
Chapter 3 47Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 48Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Gamma Distribution
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Chapter 3 49Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 50Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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.
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Chapter 3 51Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
The Weibull Distribution
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Chapter 3 52Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
When β = 1, the Weibull reduces to
the exponential
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An Application of the Weibull Distribution
Chapter 3 53Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 54Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
• 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
3.4 Probability Plots
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Normal Probability Plot
Chapter 3 55Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 56Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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The Normal Probability Plot on Standard Graph Paper
Chapter 3 57Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 58Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Other Probability Plots
• What is a reasonable choice as a probability model for these data?
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Chapter 3 59Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 60Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
3.5 Some Useful Approximations
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Chapter 3 61Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 3 62Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Learning Objectives