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Lecture_11_02

Lecture_11_02 - Lecture of Nov 2 No class on Nov 7 Tuesday...

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1 Lecture of Nov 2 Lecture of Nov 2 No class on Nov 7, Tuesday. HW#8 due on Nov 9, Thursday . HW#9 assigned and due on Nov 14, Tuesday .

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2 Chapter 5 Chapter 5 Control Charts for Variables Control Charts for Variables
3 • Quality control mainly focuses on two important statistics: - mean - variance Two Important Statistic Two Important Statistic Normal mean and variance Larger mean and normal variance normal mean and larger variance Mean is monitored by an X bar chart Variance is monitored by either a S chart (standard deviation) or an R chart (range)

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4 • Quality characteristic are generally divided into (1) variable characteristics Ch 5, chart I - III in your table (2) attribute characteristics Ch 6, chart IV - VII in the table • Also in the table, there are two scenarios for each chart: Scenario I : when the in-control mean and standard deviation are known or specified (that is, µ 0 and σ 0 are known). Scenario II : when the in-control mean and standard deviation are not known nor specified. They need to be estimated from historical data (called the training dataset or training samples ). Control Chart Table Control Chart Table
5 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 w distribution distribution parameters parameter estimate (from m training samples) µ w σ w µ ˆ w σ ˆ w x x

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Lecture_11_02 - Lecture of Nov 2 No class on Nov 7 Tuesday...

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