introduction to sqc - d montgomery - ch03 rev

Chapter 3 1Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 2Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Learning Objectives

Chapter 3 3Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

3 1 Describing VariationStem-and-Leaf Display

3.1 Describing Variation

Easy to find percentiles of the data; see page 65

Chapter 3 4Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Plot of Data in Time OrderMarginal plot produced by MINITAB

Also called a run chart

Chapter 3 5Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Also called a run chart

Histograms – Useful for large data setsHistograms 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

Chapter 3 6Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Plot frequency (or relative frequency) versus the values of the variable

Chapter 3 7Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 8Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 9Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Numerical Summary of DataNumerical Summary of DataSample average:

Chapter 3 10Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 11Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 12Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Box Plot(or Box-and-Whisker Plot)

Chapter 3 13Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Comparative Box PlotsComparative Box Plots

Chapter 3 14Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Probability DistributionsProbability Distributions

Chapter 3 15Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 16Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Sometimes called a Sometimes called a probability mass function probability density function

Will see many examples in the text

Chapter 3 17Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 18Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 19Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

20

Chapter 3 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The mean is not necessarily the 50th percentile of the distribution (that’sThe mean is not necessarily the 50 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)

Chapter 3 21Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

(that s the mode)

Chapter 3 22Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 23Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

3.2 Important Discrete DistributionsThe Hypergeometric Distribution

Chapter 3 24Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Discrete distributions are used frequently in designing acceptance sampling plans – see Chapter 15

Chapter 3 25Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 26Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Binomial Distribution

Basis is in Bernoulli trials

The random variable x is the number of successes out of n

Chapter 3 27Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Bernoulli trials with constant probability of success p on each trial

Chapter 3 28Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 29Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 30Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Poisson Distribution

Frequently used as a model for count data

Chapter 3 31Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 32Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 33Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Pascal Distribution

The random variable x is the number of Bernoulli trials upon

Chapter 3 34Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

pwhich the rth success occurs

• When r = 1 the Pascal distribution is known as• When r = 1 the Pascal distribution is known as the geometric distribution

• The geometric distribution has many useful applications in SQC

Chapter 3 35Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

3.3 Important Continuous DistributionsThe Normal Distribution

Chapter 3 36Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 37Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 38Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 39Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 40Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 41Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Practical interpretation – the sum of independent randomPractical 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 42Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Lognormal Distribution

Chapter 3 43Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 44Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 45Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Exponential Distribution

Chapter 3 46Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Relationship between the Poisson and exponential distributions

Chapter 3 47Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Gamma Distribution

Chapter 3 48Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 49Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 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.

Chapter 3 50Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Weibull DistributionThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

Chapter 3 51Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Wh β 1 thWhen β = 1, the Weibull reduces to

the exponential

Chapter 3 52Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

3 4 Probability Plots

• Determining if a sample of data might reasonably be

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 y pdistributions

• Easy to construct with computer software y p(MINITAB)

• Subjective interpretation

Chapter 3 53Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Normal Probability Plot

Chapter 3 54Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 55Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 56Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Other Probability PlotsOther Probability Plots

• What is a reasonable choice as a probability modelWhat is a reasonable choice as a probability model for these data?

Chapter 3 57Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 58Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

3.6 Some Useful Approximationspp

Chapter 3 59Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 3 60Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Learning ObjectivesLearning Objectives

Chapter 3 61Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.