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) µ w σ w µ ˆ w σ ˆ w x x ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ σ µ n , N 2 µ , σ x ˆ = µ = m x m 1 i i ∑ = µ n σ µ ˆ n ˆ σ s s ( ) σ 2 2 1 s n − ~ χ − 2 1 n σ c s ˆ 4 = σ = m s c 1 m 1 i i 4 ∑ = c 4 σ c 1 2 4 − σ c 4 σ ˆ c 1 ˆ 2 4 − σ R R complicated σ d R ˆ 2 = σ = m R d 1 m 1 i i 2 ∑ = d 2 σ d 3 σ d 2 σ ˆ d 3 σ ˆ np D Bin(n,p) p m p ˆ p m i i ∑ = = 1 np ) p 1 ( np − p n ) p 1 ( p n − p n D p ˆ = p ˆ n ~Bin(np) p m p ˆ 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 λ ) m u u ˆ m i i ∑ = = = 1 n u n u use distribution parameter estimates in expressions for µ ˆ w and σ ˆ w...
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This note was uploaded on 09/01/2011 for the course ISEN 314 taught by Professor M during the Spring '10 term at Texas A&M.

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