I have a statistics problem that I need help categorizing; that is, I need to know which branch of statistics covers the kind of problem I am trying to solve. Here is some background information:-

Today's computer chips can pack a lot transistors into a very small space. Before the computer chips get manufactured, a lot of time and energy is spent simulating via software programs how the transistor networks will perform. The reason for this is simple: manufacturing computer chips at very small geometry nodes (e.g. 32 and 22 nanometers) is incredibly expensive, so you really want to be sure the circuits perform as expected or else you will pay a lot of money to fix unexpected performance problems.

I am trying to find a statistical model that can be employed to help solve a problem in this space. Here is a little more information:-

1. When a simple circuit is created in a software program, it can look like this:-

transistor_output ---------- wire ----------- transistor_input

2. The wire is made up of a resistive component (R) and a capacitive component (C)

3. Now suppose there are n ways to describe some characteristics of the wire and what it connects to. Here are some examples:

a. the wire can be made up of multiple segments

b. the multiple segments can connect to multiple transistor_inputs

transistor_output ------|--------------------- transistor_input

transistor_input---------|

transistor_input---------|

transistor_input---------|

c. the wire(s) can be a certain length

d. the wire(s) can cover a certain amount of area

4. Now say I have x million wires in a circuit. As I mentioned above, each wire can be described n ways. I need to know the following: how many unique profiles can be derived from all the wires? By "profile" I mean if I have n = 10 or n = 20 or n = 30 ways to describe a wire, how large does n have to be before I can successfully match 50% or 60% or whatever percent of all the wires in the circuit?

Something tells me that wasn't clear enough. Here are some specific examples that might help:-

a. if I define 50 ways to describe a wire (length, width, whatever), I can find x% of the wires in a circuit that match that profile

b. if I define 60 ways to describe a wire, I can find y% of the wires that match that profile

Now what makes all of this especially difficult for me to process is that I don't know how many different ways a wire can be described. Is it 100 different ways, 500, 1000? As that number increases, what percentage of wires will match the described profile? So if a wire can be described with 1000 attributes, and I can find a whopping 20% of wires that match the profile, that's great. But if I choose to describe a wire with just 10 attributes, maybe only 0.5% of wires will match the profile, and that will be bad.

I hope this is clear enough. What kind of statistical method can be investigated to help solve this problem? This most certainly is not a case where, say, 50% of 1000 wires will match a profile made up of 500 attributes. Again, I am just looking for some high-level guidance (a specific formula would be great, of course .

Thanks,

-Keilah