IEOR 165 Lecture 16 June 26 2009

# IEOR 165 Lecture 16 June 26 2009 - given 2 of the following...

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Quality Control Overview - Xbar chart control Sample data x1…xn CASE 1 Known mean ( ) μ , variance σ2 Also define control level  = { } α P false alarm          - ~ ( , ) xbar μσn N 0 1 α = > Pxbar UCLin control α = - > - = + * . Pxbar μσn UCL μicσicn UCL μic Zα σicn We replace Zα with 2 96 % for 95 CI = β Pmissing an excursion   = < Pxbar UCLout of control = - < - Pxbar μocσocn UCL μocσocn   = < - + * PZ μic μoc Zα σicnσocn   → = + - n Zασic Zβσocμoc μic2    If we increase alpha, we need to decrease beta (vice   versa) TRADEOFF We will be given = , n ?And among multi choice we select which n is suitable ( . . , , , ) e g 40 60 80 etc = < - + * β Z μic μoc Zα σicnσocn   = Φc Given β α = < } β Pxbar UCLout of control = - < - Pxbar μocσocn UCL μocσocn = < - PZ UCL μocσocn - = - Zβ UCL μocσocn = - * UCL μoc Zβ σocn = > α Pxbar UCLin control = - > - - * Pxbar μicσicn μoc μic Zβ σocnσicn = - 1 Φc' , & , , For exam we will be given mean variance for both to find alpha beta . n OR we will be

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Unformatted text preview: : , , . given 2 of the following alpha beta n Summarized: Xbar chart control (exam definite)-Case 1: , , = + * = - * μ σ2known so UCL μ 3 σn and LCL μ 3 σn if data in , this interval then in control-Case 2 , μ σ2unknown so we calculate sample mean & sample var for each set of data. Then average it. = + … xbar xbar1 xbar2 xbarkk = + +… Sbar Sbar1 Sbar2 Skk = + * * =- * * UCL xbar 3 Sbarn cn and LCL xbar 3 Sbarn cn S Chart Control (hw only)-σ2known = * ESi σ cn =-Si σ21 c2n ± ( -( ) n 3σ2 1 c2 n -σ2unknown-Estimate σ bySbarcn-±- Sbar 3Sbar1c2n 1 --Fraction Defective Control (exam definite)-Fraction defective prob. as p. -p is known-= =-EF P VarF p1 pn -p1 pn is the fraction. Total # defective: ±-np Zαp1 pn-p unknown-Use estimator for p:-Estimate p by Fbar ±-Fbar 3Fbar1 Fbarn--...
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IEOR 165 Lecture 16 June 26 2009 - given 2 of the following...

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