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Lecture_10_24

# Lecture_10_24 - Mid Term Stats Histogram 10 9 8 7 6 5 4 3 2...

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1 Mid Term Stats Mid Term Stats Histogram 1 4 8 9 4 3 0 1 2 3 4 5 6 7 8 9 10 Frequency 15 20 26 28 30 24 mean: 24.05/30 median: 25/30 highest: 30/30 stdev: 4.07

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2 Lecture of Oct 24 Lecture of Oct 24 Last Class Lab session resumes on Friday. HW#7 assigned today and due Tuesday, Oct 31. U pper C ontrol L imit C enter L ine L ower C ontrol L imit n z LCL CL n z UCL 0 2 / 0 0 0 2 / 0 σ µ = µ = σ + µ = α α - why choose α = 0.0027?
3 General Model General Model General Model for Control Charts : Suppose that we are periodically collecting samples of data and calculating some sample statistic that we will denote by w . For example, for normal distribution data w = x , average w = s 2 , variance w = R = max( x j ) - min( x j ), range for Poisson data, w = λ average number of defects per unit for Binomial data, w = p , count of nonconforming units

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4 General Model General Model Control chart for w is to plot w versus the sample sequence number and add appropriate control limits as w w w w w L LCL CL L UCL σ µ = µ = σ + µ = where µ w and σ w denote the mean and standard deviation of w when the process is truly in control, and L is some constant value we need to choose to set the control limits (for instance, we chose L =3 before).
5 General Model General Model A control chart on w will be viewed as a sample-by-sample series of hypothesis tests of H 0 : the current mean of w = in-control mean µ w H 1 : the current mean of w in-control mean µ w H 1 implies that the process is out of control.

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