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3_Control Chart Basics

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

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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. Scatter Diagram 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) t t 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 (shift in mean) t t t t t t t * œ   œ . 5% . $ 5% X (shift in variance) t t t t t t t * œ   œ . 5% . $5% X (linear trend in mean) t t t t t t t t * œ   œ . 5% . α " 5% X (correlation in observations) t t (X t t t t t 1 t * œ Ñ    œ . 5% . 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 • On Chart 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. • Use 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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