4_Ctlchart

4_Ctlchart - Lecture Notes - OR 182, 282 Quality Control...

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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 1 1 CONTROL CHART BASICS PRELIMINARIES Basic Vocabulary • Statistical Process Control (SPC) - collection of problem solving tools useful in achieving process stability and improving capability through reduced variation. - tools include (The Magnificent Seven) 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 - one that operates with only chance variation
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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 2 2 • Assignable Cause - a sourse of variation external to the process caused by wearing machinery, operator error, defective raw materials, etc. - usually larger than the chnace variation - usually exhibits itself via 1. Sudden or prolonged shift in mean 2. Sudden or prolonged shift in variance 3. Sudden or prolonged shift in correlation among observations STATISTICAL BASIS FOR CONTROL CHARTS
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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 3 3 Relationship between control charts and hypothesis tests • Control Charts for soemCharacteristic A - Control limits L œ„ .5 AA UCL LCL Process Mean - small probability outside bounds - False Alarm vs. Quick Res. - IID Assumption - Checks the Validity of Stable Meaan and Variance “A process not in statistical control does not have a stable distribution" Ê
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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 4 4 • Hypothesis Tests - If X ~ N( , ) Examples .5 # known X ~ N( , n) N(0,1) ^ 5. . 5 Êœ Î Ê µ # 8 X / . 5 È For hypothesis testing H vs H : !! + ! Àœ Á .. Type I error Pr{Fail to Accept H | } α. . œœ 1 P r { z z | } œ Ÿ Ÿ œ αα . 5 ÎÎ 8 ! 22 X / ! È Type II error Pr{Accept H | } ". . ! a P r { z z | } Ÿ Ÿ œ . 5 8 X / a ! È P r { z z | } Ÿ Ÿ œ . 55 5  88 8 aa a // / X a ÈÈ È P r { z Z z | } Ÿ Ÿ œ a z z œ FF Š‹
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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 5 5 - think of the control chart as several hypothesis tests • Reality vs. Theory - The assumed model is X tt œ .5 % where N(0,1) Pr{ X – 3 } = .0027 %. 5 µÊ ± ±   - , unknown but estimated - actual distribution of unknown, % t sample means used approximate normality Ê (ok if approx symmetric and bell shaped or transformable) - term “Probability" not used instead “3 limit" but L could be based ß 5 on sigma (L 3) or probability (L z ) limits œœ α Î 2
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Lecture Notes - OR 182, 282 Quality Control and Acceptance Sampling - Professor Jim Harris - 6 6 Setting Up - Control Charts cannot alone produce control • Procedure - Inital Data used to determine control limits - Use some 20 25 subgroups of 4 to 6 samples (or 50 for single observation charts) - Data most be recent enough to represent current process - Grouping must be relevant.
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This note was uploaded on 01/02/2010 for the course EMSE 282 taught by Professor Harris during the Spring '07 term at GWU.

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4_Ctlchart - Lecture Notes - OR 182, 282 Quality Control...

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