introduction to sqc - d montgomery - unit 002
DESCRIPTION
Introduction to SQC - D Montgomery - Unit 002TRANSCRIPT
![Page 1: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/1.jpg)
1
Chapter 2 2Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 2: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/2.jpg)
2
Chapter 2 3Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Learning Objectives
Chapter 2 4Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
•Easy to find percentiles of the data; see page 43
Stem-and-Leaf Display
![Page 3: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/3.jpg)
3
Chapter 2 5Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
•Also called a run chart
Marginal plot produced by MINITAB
Plot of Data in Time Order
Chapter 2 6Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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
![Page 4: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/4.jpg)
4
Chapter 2 7Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Histogram for discrete
data
Chapter 2 8Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 5: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/5.jpg)
5
Chapter 2 9Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Numerical Summary of Data
Chapter 2 10Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 6: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/6.jpg)
6
Chapter 2 11Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 12Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Box Plot(or Box-and-Whisker Plot)
![Page 7: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/7.jpg)
7
Chapter 2 13Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Comparative Box Plots
Chapter 2 14Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Probability Distributions
![Page 8: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/8.jpg)
8
Chapter 2 15Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 16Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Will see many examples in the text
Sometimes called a probability mass function
Sometimes called a probability density function
![Page 9: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/9.jpg)
9
Chapter 2 17Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 18Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 10: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/10.jpg)
10
Chapter 2 19Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 20Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 11: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/11.jpg)
11
Chapter 2 21Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 22Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 12: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/12.jpg)
12
Chapter 2 23Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 24Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Hypergeometric Distribution
![Page 13: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/13.jpg)
13
Chapter 2 25Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 26Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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
![Page 14: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/14.jpg)
14
Chapter 2 27Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 28Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 15: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/15.jpg)
15
Chapter 2 29Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 30Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Frequently used as a model for count data
The Poisson Distribution
![Page 16: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/16.jpg)
16
Chapter 2 31Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 32Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The random variable x is the number of Bernoulli trials upon which the rth success occurs
The Pascal Distribution
![Page 17: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/17.jpg)
17
Chapter 2 33Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
• When r = 1 the Pascal distribution is known as the geometric distribution
• The geometric distribution has many useful applications in SQC
Chapter 2 34Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Normal Distribution
![Page 18: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/18.jpg)
18
Chapter 2 35Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 36Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 19: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/19.jpg)
19
Chapter 2 37Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 38Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Original normal distribution
Standard normal distribution
![Page 20: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/20.jpg)
20
Chapter 2 39Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 40Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 21: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/21.jpg)
21
Chapter 2 41Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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
Chapter 2 42Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Lognormal Distribution
![Page 22: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/22.jpg)
22
Chapter 2 43Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 44Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 23: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/23.jpg)
23
Chapter 2 45Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Exponential Distribution
Chapter 2 46Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Relationship between the Poisson and exponential distributions
![Page 24: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/24.jpg)
24
Chapter 2 47Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Gamma Distribution
Chapter 2 48Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
• The gamma distribution has many applications in reliability engineering; see Example 2-121, text page 71
• When r is an integer, the gamma distribution is the result of summing r independently and identically exponential random variables each with parameter λ
![Page 25: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/25.jpg)
25
Chapter 2 49Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Weibull Distribution
Chapter 2 50Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
• When β = 1, the Weibull distribution reduces to the exponential distribution
![Page 26: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/26.jpg)
26
Chapter 2 51Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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
Chapter 2 52Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Normal Probability Plot
![Page 27: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/27.jpg)
27
Chapter 2 53Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 54Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Other Probability Plots
• What is a reasonable choice as a probability model for these data?
![Page 28: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/28.jpg)
28
Chapter 2 55Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 56Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
![Page 29: Introduction to SQC - D Montgomery - Unit 002](https://reader034.vdocuments.mx/reader034/viewer/2022052321/554a58beb4c905572f8b4df4/html5/thumbnails/29.jpg)
29
Chapter 2 57Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 2 58Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Learning Objectives