## Friday, October 28, 2005

### Statistical Fluctuations and Dependant Events

The author explains the concept of statistical fluctuations and dependant events very nicely using the Marching Scouts example.

Imagine a single queue of marching kids in a straight line with the leader at the beginning with other kids behind him. The goal is to transport all kids from point A to point B. Since no one can over take any one else, the speed of any kid cannot be faster than the kid in front of him. Therefore if the slowest kid - Charlie is walking much slower than the kid in front of him, the gap between them will increase. The kids behind Charles - even if faster than Charles will be limited to his speed.
This makes transporting all kids from point A to point B dependant on Charles speed.
However, intermittently, Charles (and other slow kids) will run up a little to catch up with the kid in front of them. Therefore the speed is never constant.

Applying this analogy to a production line, Charles is the bottle neck and the throughput of the entire line depends on the throughput of the bottleneck. As the speed of each kid is dependant on speed of kids ahead of him, this is the dependant events.
Just like the speed of the kids is not always same, production process is not always at the same speed. This is the statistical fluctuation.
Each kid, who is slower than the kid in front of him, is adding to the distance between the first scout and last scout. Therefore the statistical fluctuations add up. They do not average out.
There will always be someone who is the slowest; similarly there will always be a bottle neck in the system.

ZajeRulEZ said...

herbie is the bottle neck!!!! read the book again!

8:16 AM
Canaan said...

Excellent explanation!

9:23 PM
Ajmal Abdullah said...

good explanation but it's just so funny as Herbie is the obvious bottleneck. Mentioned several times in the book

1:35 AM