introduction to sqc - d montgomery - unit 002

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

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Learning Objectives


•Easy to find percentiles of the data; see page 43

Stem-and-Leaf Display

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•Also called a run chart

Marginal plot produced by MINITAB

Plot of Data in Time Order


•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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Histogram for discrete

data


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Numerical Summary of Data


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

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Comparative Box Plots


Probability Distributions

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Will see many examples in the text

Sometimes called a probability mass function

Sometimes called a probability density function

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The Hypergeometric Distribution

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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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Frequently used as a model for count data

The Poisson Distribution

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The random variable x is the number of Bernoulli trials upon which the rth success occurs

The Pascal Distribution

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

• The geometric distribution has many useful applications in SQC


The Normal Distribution

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Original normal distribution

Standard normal distribution

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• Practical interpretation – the sum of independent random variables is approximately normally distributed regardless of the distribution of each individual random variable in the sum


The Lognormal Distribution

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The Exponential Distribution


Relationship between the Poisson and exponential distributions

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The Gamma Distribution


• 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

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The Weibull Distribution


• When β = 1, the Weibull distribution reduces to the exponential distribution

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• 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


Normal Probability Plot

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Other Probability Plots

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

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Learning Objectives

introduction to sqc - d montgomery - unit 002

Engineering