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ENV 2006 CS3.2
Multidimensional Detective
• Parallel coordinate plots can initially be intimidating
Excellent worked example provided by the creator:A. Inselberg, Multidimensional Detective, IEEE Visualization 1997
ENV 2006 CS3.3
Understand the Problem
• What is the data?– 473 batches of a VLSI chip– 16 process parameters: X1,..X16– Yield (% useful in batch): X1– Quality (speed): X2– Defects (zero at top): X3 to X12– Physical parameters: X13 to X16
• What is the objective?– Raise the yield, X1– Maintain the quality, X2
• How achieved?– Minimize the defects
Why are we using visualization?
We seek relationships amongst the variables
ENV 2006 CS3.4
Brushing
• Brushing can select observations which are high in X1 and X2
• Notice separation into two classes in X15
• Some high X3 are not selected
Principle 1: Do not let the picture intimidate youPrinciple 2: Understand the objectives and use them to obtain ‘visual cues’Principle 3: Carefully scrutinise the picture
ENV 2006 CS3.5
Look at the other defect categories
• Now look for batches with zero defects in 9 out of the 10 defect categories
• Inselberg calls the result a ‘shocker’! Why?
ENV 2006 CS3.6
Back to the Drawing Board
• Return to base camp
• X6 is clearly different from the other defect categories
• So try excluding X3 and X6 – leaving 8 defect categories
.. Now we do get the high yield batch
ENV 2006 CS3.7
Good batches
• The best batch has all zeroes except for X3 and X6
• So.. Are these measurement errors in X3 and X6?
• Look for the top group of batches
• None have zero defects in X3 or X6
Principle 4: Test the assumptions and especially the ‘I am really sure of ..’ s