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Pascals Triangle, Home Work and Root Cause Analysis Expand / Collapse
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Posted Wednesday, October 19, 2011 12:14 AM
SSCrazy

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Comments posted to this topic are about the item Pascals Triangle, Home Work and Root Cause Analysis

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Post #1192655
Posted Wednesday, October 19, 2011 2:06 AM


Ten Centuries

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Excellent article.

Even better, I see you used to work in Manchester!


Paul.
Manchester,UK.
Post #1192689
Posted Wednesday, October 19, 2011 7:18 AM
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I enjoyed your article because it was relevant on multiple levels. Thank you for a well-written article!
Post #1192835
Posted Wednesday, October 19, 2011 7:50 AM
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Hi David,

This is fantastic! I can find many uses for this..


Thanks!


John R
Post #1192853
Posted Wednesday, October 19, 2011 8:10 AM
Ten Centuries

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Good article.

Of course, the point you omitted is how the actual probability of any given failure alters the calculations.

With the lottery example, because each of the numbers is (supposedly) equally likely to be chosen, Pascal's triangle is a perfect model, and shows the true (im)probability of winning.

With the car example, QA testing ensures that parts generally have a much higher probability of working than failing, thus although there's only one way for the whole system to work perfectly, it's more likely than the millions of ways it can fail.
Post #1192869
Posted Wednesday, October 19, 2011 9:50 AM
SSCrazy

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Yes, and apparently each space shuttle launch expected at least 6000 components to fail but was still designed to work.

On my list of things not to think about is precisely how fast a piece of metal moves inside a motor-bike engine when it's between your legs


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Post #1192977
Posted Wednesday, October 19, 2011 11:04 AM


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I think you got trapped in teh procedural mindset. I would use a look up table with DECIMAL(s, 0) columns so i can get the range I need. Ther is one for 1 to 23! at

http://membres.multimania.fr/rsirdey/facttabl.htm

Now, we can apply a little algebra in a CASE expression instead of brute force:
CREATE FUNCTION Perm(@n DECIMAL, @r DECIMAL)
RETURNS DECIMAL (s,0)
AS
RETURN
CASE WHEN @r = (0, @n) THEN 1.0
WHEN @r = 1.0 THEN @n
THEN (SELECT fact FROM Factrorials
WHERE @f = @n)
/ (SELECT fact FROM Factrorials
WHERE @f = (@n-@r)
ELSE CAST (NULL AS DECIMALs,0)) END;




Books in Celko Series for Morgan-Kaufmann Publishing
Analytics and OLAP in SQL
Data and Databases: Concepts in Practice
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SQL for Smarties
SQL Programming Style
SQL Puzzles and Answers
Thinking in Sets
Trees and Hierarchies in SQL
Post #1193052
Posted Wednesday, October 19, 2011 12:17 PM
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Joe, I should have remembered that. I think one of your books mentioned storing a calendar table rather than trying to workout calendar maths on the fly.

It is so easy to forget that storing a few thousand records for utility sets costs next to nothing but delivers one hell of a lot of utility


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Post #1193120
Posted Wednesday, October 19, 2011 1:34 PM


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Thanks for the great article. It reminds me of why when I used to fly airplanes my instructor kept telling me that the probability of an engine failure in a twin engine plane was twice as high as a single... of course you still had one engine running in a twin.

do it right, or do it over and over, it's up to you
Post #1193190
Posted Wednesday, October 19, 2011 3:10 PM
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Don't you also need to make sure that @n <> @r so you don't divide by 0? And @r <> 0 either.
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