So I'm working on calculating how breakage rates impact manufacturing. Running into a fairly interesting problem:
I have three steps in the process, A, B, and C. The process (generally, not always) goes A->B->C. Each has an associated weight with how many units end up going through each step. Let's call it A%, B%, and C%.
As an example, let's say I'm making 100k widgets. A% = 90%, B% = 80%, and C% = 100%. So A has 90k widgets go through, B has 80k widgets go through, and C has 100k widgets go through.
Now, each step has two different types of chances of breaking.
A_Full_Break%
A_Step_Break%
B_Full_Break%
B_Step_Break%
C_Full_Break%
C_Step_Break%
Now, if the item breaks in a full break %, it's sent back to go, it needs to restart the entire process over. If it just has step break %, it just needs to redo the same step.
Since A is the first step, naturally one of the two steps is 0%. An argument could be made for either one, and really, it's whatever is easier to think of it as.
Now, A, B, and C each have a Raw Equipment Capacity. Let's call it A_REC, B_REC, and C_REC. What I'm trying to figure out is what the actual capacity is. A simple example would be: If I only have one step, A_REC, and the capacity was 100k widgets, with a 10% breakage rate, I'd have a real capacity of 90k widgets, since 10k of them would break. What I'm trying to solve is, how do I calculate the real capacity of my steps, in general terms, given that some units get sent back through, break again, get sent back, could break at a different step, might break at that step but just need a redo, etc. This looks like it should be easy to calculate, but it's been driving me nuts trying to make it work.
(The actual problem I'm working on has 15 steps and a few more twists, but I think I've got a solid handle on those parts, and can extrapolate an answer...)