Lec 12 - Attributes Control Charts

Lec 12 - Attributes Control Charts - Attributes Control...

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Attributes Control Charts Variables Control Charts for continuous measurements Attribute Control Charts for discrete measurements
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P Charts for Fraction Defective Monitors fraction defective Defective is unusable fraction of broken glass plates fraction of defective chips on a wafer fraction of defective truffle shells go-no-go gauge 2
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P Chart Based on Binomial Distribution sample size n for sample i X i = number of defectives in sample of n p = fraction defective in pop’ln = P(unit is defective) r.v. X Binomial(n, p) P(X x = 0,1, . .. , n i i = = - - x n x p p x n x ) ( ) 1 E(X)=np V(X)=np(1-p) 3
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Sample Statistic is Fraction Defective At each sample time plot p x n i i = Note: E p n E x p V p n V x np p n p p n i i i i ( ) ( ) ( ) ( ) ( ) ( ) = = = = - = - 1 1 1 1 2 2 Control Limits UCL p p p n LCL p p p n = + - = - - 3 1 3 1 ( ) ( ) CL = p 4
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Some Notes on P Charts If LCL is negative, make it zero Test statistic is not normal - don't use zone rules If p i = 0, process in-control 5
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Data: draw m (say 20) subsamples of size n X 1, X 2 , . .. , X m Sample Statistics: p 1, p 2 , . .. , p m Estimate for CL = p p x x nm m = + + 1 ... 6
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This note was uploaded on 09/20/2011 for the course ENG 300 taught by Professor Albin during the Fall '11 term at Rutgers.

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Lec 12 - Attributes Control Charts - Attributes Control...

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