Pascals Triangle, Home Work and Root Cause Analysis

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Pascals Triangle, Home Work and Root Cause Analysis

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David.Poole

Posted Wednesday, October 19, 2011 12:14 AM

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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

paul s-306273

Posted Wednesday, October 19, 2011 2:06 AM

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Excellent article.

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

Paul.
Manchester,UK.

Post #1192689

Carla Wilson-484785

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

eephus101

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

sknox

Posted Wednesday, October 19, 2011 8:10 AM

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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

David.Poole

Posted Wednesday, October 19, 2011 9:50 AM

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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 Tongue

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Post #1192977

CELKO

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 DECIMAL Sad

s,0)) END;

Books in Celko Series for Morgan-Kaufmann Publishing
Analytics and OLAP in SQL
Data and Databases: Concepts in Practice
Data, Measurements and Standards in SQL
SQL for Smarties
SQL Programming Style
SQL Puzzles and Answers
Thinking in Sets
Trees and Hierarchies in SQL

Post #1193052

David.Poole

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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richard.rabe

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

pmcpherson

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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