# Lecture 4 - IE 330 Industrial Quality Control Lecture 4 A...

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IE 330 Industrial Quality Control Lecture 4: A quick review of concepts in probability and statistics 1/28/2008

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Binomial Distribution Assume that we produce fair coins We need to make sure they are really fair Take 10 samples every 30 minutes
Inferences from samples Sample 1 0 1 1 1 0 0 1 1 1 1 1 0.727273 0.467099 Sample Mean ample standard deviatio

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Process control and sampling Control Chart 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 2 3 4 5 6 7 8 9 10 Sample no Sample mea 1) Confidence level 2) When to take action 3) How about variance
Prerequisite Probability knowledge Histogram Discrete and Continuous distributions Discrete: Binomial, Bernoulli, and Poisson Continuous: Exponential, Normal Random Variable PDF, PMF, CDF Conditional distribution and Law of total probability Total probability law

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Control chart idea Check if a process is under control Produces the same product, statistically Sample Look for abnormalities???
Samples Could be from any distribution But we have SLLN and CLT SLLN CLT

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Illustrate CLT
Normal Probability Plots Normal Distribution Normal Distribution Figure 1 shows a certain normal distribution and depicts a random sample of ten observations X drawn from that normal distribution. Figure 1 Normal Distribution

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Goodness of fit tests We are interested in knowing whether these data might have arisen from a process which follows the normal distribution.
Normal Probability Plots Figure 2 Figure 2 X versus P(X) P(X): The cdf of normal For the normal distribution P(X) has the ''S'' shaped curve shown in the figure. P(x) X Figure 2 Linear Graph Paper

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Normal Probability Plots Figure 3 Figure 3 Here the scale for P(X) has been adjusted so that for a random sample from a normal distribution the plot of X versus P(X) is a straight line. P(x) X Figure 3 Normal Probability Paper
Normal Probability Plots Test for Normality Test for Normality The adjustment of the P(X) scale as shown in Figure 3 produces a special graph paper which we refer to as Normal Probability Paper. There are many instances in which we might like to know whether a certain set of data follow (behave as) the normal distribution. Normal Probability Paper provides a simple graphical technique to test for normality of a set of data.

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Normal Probability Plots Example: Construction Of A Normal Probability Plot Example: Construction Of A Normal Probability Plot Suppose that we have obtained the following measurements (in coded form): -1.50, 0.50, -0.75, -0.25, 0.50, 1.75, 1.25 We are interested in knowing whether these data might have arisen from a process which follows the normal distribution.
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