general control chart model

general control chart model - w distribution distribution...

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1 General Control Chart Model (for charting statistic w, with L-sigma control limits): Distribution Parameters Known Distribution Parameters Unknown UCL = µ w + L σ w UCL = µ ˆ w + L σ ˆ w CL = µ w CL = µ ˆ w LCL = µ w – L σ w LCL = µ ˆ w – L σ ˆ w D = # defective items in sample of size n items x = # defects in one sample (one sample equals one inspection unit for c-charts and n inspection units for u-charts) General formulae for alpha and beta error, given LCL and UCL (use w and appropriate distribution from above table): α = P{w UCL or w LCL | in-control distribution parameter} = 1 – P{w < UCL | in-control distribution parameter} + P{w LCL | in-control distribution parameter} β = P{LCL < w < UCL | out-of-control distribution parameter} = P{w < UCL | out-of-control distribution parameter} – P{w LCL | out-of-control distribution parameter} chart type
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Unformatted text preview: w distribution distribution parameters parameter estimate (from m training samples) w w w w x x n , N 2 , x = = m x m 1 i i = n n s s ( ) 2 2 1 s n ~ 2 1 n c s 4 = = m s c 1 m 1 i i 4 = c 4 c 1 2 4 c 4 c 1 2 4 R R complicated d R 2 = = m R d 1 m 1 i i 2 = d 2 d 3 d 2 d 3 np D Bin(n,p) p m p p m i i = = 1 np ) p 1 ( np p n ) p 1 ( p n p n D p = p n ~Bin(np) p m p p m 1 i i = = p n ) p 1 ( p p n ) p 1 ( p c x Pois(c) c m x c m 1 i i = = c c c c u n x u = x~Pois(n ) m u u m i i = = = 1 n u n u use distribution parameter estimates in expressions for w and w...
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