3_Control Chart Basics

3_Control Chart Basics - Spring 2008 EMSE 182, 282,...

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Spring 2008 EMSE 182, 282, Professor Jim Harris, Control Chart Basics - 1 CONTROL CHART BASICS PRELIMINARIES Basic Vocabulary • Statistical Process Control (SPC) collection of problem solving tools useful in achieving process Ä stability and improving capability through reduced variation. tools include (The Magnificent Seven) Ä 1. Histogram 2. Check Sheets 3. Pareto Diagram 4. Cause and Effect Diagram 5. Defect Concentration Diagram 6 . S c a t t e r D i a g r a m 7. Control Chart • A Process "In Control" one that has a stable mean and variance Ä one that operates with only chance variation Ä mathematically represented by Ä X , where { } are iid with ~ N(0,1) tt t t œ .5 % % %
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Spring 2008 EMSE 182, 282, Professor Jim Harris, Control Chart Basics - 2 • Assignable Cause a source of variation external to the process caused by wearing Ä machinery, operator error, defective raw materials, etc. usually larger than the chance variation Ä a process operating in the presence of one or more assignable causes Ä is said to be "out of control" usually exhibits itself via Ä 1. sudden or prolonged shift in mean 2. sudden or prolonged shift in variance 3. sudden or prolonged shift in correlation among observations example models of assignable cause at t Ä X ( s h i f t i n m e a n ) tt t t t * œ     œ .5 % .$5 % X ( s h i f t i n v a r i a n c e ) t t t * œ   œ % .$ 5 % X (linear trend in mean) t t t t * œ   œ % .α" 5 % X (correlation in observations) (X t t t t t1 t * œ  Ñ   œ % .9 . 5 %
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Spring 2008 EMSE 182, 282, Professor Jim Harris, Control Chart Basics - 3 STATISTICAL BASIS FOR CONTROL CHARTS Basic Design O n C h a r t data plotted and connected with line segments Ä center line, upper and lower control limits (UCL and LCL), and Ä sometimes upper and lower warning limits plotted on chart. U s e process is out-of-control, look for assignable cause when Ä 1. any point plots outside the control limits outside 2. certain runs criteria are observed 3. any pattern in data is observed
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Spring 2008 EMSE 182, 282, Professor Jim Harris, Control Chart Basics - 4 Relationship between control charts and hypothesis tests • Control Charts for Some Characteristic A control limits L Äœ .5 AA similarities to hypothesis testing Ä think of the control chart as several hypothesis tests 1. observe statistic x from data A 2. compare to acceptance region [ L L ]  , 3. each plot tests H : vs H : !A A .. œÁ 1 4. process continues (fail to reject null hypothesis) if x [ L L ] (acceptance region) A A A − , and is stopped (reject null hypothesis) if it is not 5. may incorrectly stop process and look for assignable cause when none exists (Type I error) and may not get an out of control signal when one exists (Type II error)
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Spring 2008 EMSE 182, 282, Professor Jim Harris, Control Chart Basics - 5 6. trade offs false alarm (significance level, ) vs. quick response α (power, 1 ). " 7. a plot of power 1
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3_Control Chart Basics - Spring 2008 EMSE 182, 282,...

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