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Introduction to SQC - D Montgomery - Unit 002
 

Introduction to SQC - D Montgomery - Unit 002

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Introduction to SQC - D Montgomery - Unit 002

Introduction to SQC - D Montgomery - Unit 002

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    Introduction to SQC - D Montgomery - Unit 002 Introduction to SQC - D Montgomery - Unit 002 Document Transcript

    • 1 Chapter 2 2Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. Copyright (c) 2005 John Wiley & Sons, Inc.
    • 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
    • 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
    • 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.
    • 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.
    • 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)
    • 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
    • 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
    • 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.
    • 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.
    • 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.
    • 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
    • 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
    • 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.
    • 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
    • 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
    • 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
    • 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.
    • 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
    • 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.
    • 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
    • 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.
    • 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
    • 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
    • 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
    • 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
    • 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?
    • 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.
    • 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