I have a real-world situation with a machine that lays a layer of wires on a high-pressure hose. The machine has S "slots" (approx 200), and each slot could have one wire or be empty. Typically there are about 100 - 180 wires (W). The objective is to uniformly distribute the wires over the slots, so the best hose is manufactured. The company uses a schedule on how to put the wires on the machine. For each value of W it shows how to distribute the wires. This distribution has been used for two decades or more "because we always done things that way". I came up with a different and I think more uniform distribution calculation using my Excel programming skills. Now I want to mathematically prove mine is better. My question is how to do that. Example of company distribution with S=144 and W=80: (1 indicates a slot with wire present; 0 is an empty slot) A section of 17: 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 with 6 evenly distributed sections of 1 0 1 0 1 0 1 My solution: 1 0 1 0 1 0 1 0 1 (divide both numbers by 16, then it becomes a "distribute 5 in 9" question) There must be some way to calculate the evenness of distribution. One thought I had is that an even distribution has the same percentage of 1's regardless of the size of the sample. Can you point me in the right direction? Thanks, Tom in Phoenix.
How to quantify uniform distribution?
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probability-distributions
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0When you say "uniform" do you mean you want everything to be as evenly spaced as possible? (In mathematics "uniform" sometimes means "every possibility happens with equal probability" which is actually very different from "evenly spaced.") – 2011-07-30
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1Also, it's not clear to me how to "mathematically prove" that your distribution is better without knowing why and in what way a more even spacing of the wires leads to a better product. – 2011-07-30
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0Yes, evenly spaced. Even spacing leads to more even spacing of the wires on the hose, less tangling, less wires on top of each other. – 2011-07-30
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1Then isn't there some kind of performance test you can do on the different distributions? That seems like it would be more convincing than a mathematical argument in this context. – 2011-07-30
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Yes we are now building a few test hoses using my distribution. They are then tested at above 20,000 PSI until they burst. The math proof was more to satisfy my curiosity. – 2011-07-30