Transcription
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.1
Learning ObjectivesChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.2
3.1 Describing VariationStem-and-Leaf DisplayEasy to find percentiles of the data; see page 69Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.3
Plot of Data in Time OrderMarginal plotproduced byMINITABAlso called a run chartChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.4
Histograms – Useful for large data setsGroup values of the variable into bins, then count the numberof observations that fall into each binPlot frequency (or relative frequency) versus the values ofthe variableChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.5
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.6
Additional Minitab GraphsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.7
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.8
Numerical Summary of DataSample average:Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.9
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.10
The Standard DeviationChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.11
The Box Plot(or Box-and-Whisker Plot)Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.12
Comparative Box PlotsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.13
Probability DistributionsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.14
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.15
Sometimes called aprobability mass functionSometimes called aprobability density functionWill see many examples in the textChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.16
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.17
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.18
The mean is the point at which the distribution exactly “balances”.Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.19
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 randomvariable (that’s the mode)Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.20
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.21
3.2 Important Discrete DistributionsThe Hypergeometric DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.22
Discrete distributions are used frequently in designing acceptancesampling plans – see Chapter 15Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.23
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.24
The Binomial DistributionBasis is in Bernoulli trialsThe random variable x is the number of successes out of nBernoulli trials with constant probability of success p on each trialChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.25
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.26
Binomial DistributionsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.27
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.28
The Poisson DistributionFrequently used as a model for count dataChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.29
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.30
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.31
The Negative Binomial DistributionThe random variable x is the number of Bernoulli trials uponwhich the rth success occursChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.32
The negative binomial distribution is alsosometimes called the Pascal distribution When r 1 the negative binomial distribution isknown as the geometric distribution The geometric distribution has many usefulapplications in SQCChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.33
Geometric DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.34
3.3 Important Continuous DistributionsThe Normal DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.35
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.36
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.37
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.38
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.39
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.40
The Central Limit TheoremPractical interpretation – the sum of independent randomvariables is approximately normally distributed regardless ofthe distribution of each individual random variable in the sumChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.41
The Lognormal DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.42
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.43
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.44
The Exponential DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.45
Relationship between the Poisson and exponential distributionsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.46
Lack-of-memory propertyChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.47
The Gamma DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.48
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.49
When r is an integer, the gamma distribution is the result of summing rindependently and identically exponential random variables each withparameter λ.The gamma distribution has many applications in reliability engineering.Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.50
The Weibull DistributionChapter 3Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2012 John Wiley & Sons, Inc.51
When β 1, theWeibull reduces tothe exponentialChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.52
An Application of the Weibull DistributionChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.53
3.4 Probability Plots Determining if a sample of data might reasonably beassumed to come from a specific distribution Probability plots are available for variousdistributions Easy to construct with computer software(MINITAB) Subjective interpretationChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.54
Normal Probability PlotChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.55
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.56
The Normal Probability Plot on Standard Graph PaperChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.57
Other Probability Plots What is a reasonable choice as a probability modelfor these data?Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.58
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.59
3.5 Some Useful ApproximationsChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.60
Chapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.61
Learning ObjectivesChapter 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.Copyright (c) 2013 John Wiley & Sons, Inc.62
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