Six-Sigma10 - Analyze Phase 1 Analyze Phase Elements...

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Analyze Phase 1
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Analyze Phase Elements Select Analysis Tools Use Analysis Tools Identify Sources of Variation
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Analyze Basic Tools and Methods Measuring and modeling the relationship between Variables Hypothesis Testing Failure mode and effects analysis (FMEA) Additional Methods
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Example
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1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 100 98 96 94 92 90 88 86 HydroCarbon Purity S 1.08152 R-Sq 87.8% R-Sq(adj) 87.1% Fitted Line Plot Purity = 74.30 + 14.93 HydroCarbon
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Simple Linear Regression
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0 20 40 60 02 0 4 0 6 0 X Y Scattergram • 1. Plot of All ( X i , Y i ) Pairs • 2. Suggests How Well Model Will Fit
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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0 20 40 60 02 0 4 0 6 0 X Y How would you draw a line through the How would you draw a line through the points? How do you determine which line points? How do you determine which line fits best fits best ? ? Thinking Challenge
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Least Squares Graphically ε 2 Y X 1 3 4 ^ ^ ^ ^ 2 Y X 1 3 4 ^ ^ ^ ^ YX 20 1 2 2 =+ + $$ $ ββ 1 2 2 + $ $ ii 01 $ LS minimizes $ $$$$ εεεε i i n 2 1 1 2 2 2 3 2 4 2 = +++ = $ i i n 2 1 1 2 2 2 3 2 4 2 = =
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Least Squares Using Equation 11-2, t he n observations in the sample can be expressed as The sum of the squares of the deviations of the observations from the true regression line is
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Linear Regression by Least Squares
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Linear Regression by Least Squares
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Coefficient Equations Sample Slope Sample Slope Sample Y Sample Y - - intercept intercept Prediction Equation Prediction Equation x y 1 0 ˆ ˆ β = ( ) ( ) () = = 2 1 ˆ x x y y x x SS SS i i i xx xy i i x y 1 0 ˆ ˆ ˆ β+=
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Simple Linear Regression Example 11-1
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Simple Linear Regression Example 11-1
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1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 100 98 96 94 92 90 88 86 HydroCarbon Purity S 1.08152 R-Sq 87.8% R-Sq(adj) 87.1% Fitted Line Plot Purity = 74.30 + 14.93 HydroCarbon
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Population Model Figure 11-2 The distribution of Y for a given value of x for the oxygen purity-hydrocarbon data.
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11-4 Hypothesis Tests in Simple Linear Regression 11-4.1 Use of t -Tests We would reject the null hypothesis if
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This note was uploaded on 05/09/2010 for the course IE IE7610 taught by Professor Dr.kaiyang during the Winter '10 term at Wayne State University.

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Six-Sigma10 - Analyze Phase 1 Analyze Phase Elements...

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