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Perhaps percentages confuse the issue?
They usually do :-)
What are they percentages of? Why are they in a fixed ratio? It's easier to tell whether you're doing the right maths (and the maths right) when you know what the numbers actually mean.
If I'm machining a 3:2:1 tooling block with sides A B and C, and I want to make sure it weighs D, a set of equations of the form
A=3C
B=2C
D=kABCwill work, and that's what you've got. I set k as the density and can find the lengths of the sides for any arbitrary target weight, but the last equation always simplifies to
D=6kC³
because the variables A B and C are not independent. It seems unlikely that your quality system would need 3 variables on the input side if they are not independent.
Let's say I want 90% of my headset covers to be saleable. There is a boring operation, an OD turning operation and a parting off height operation. The probability P0 that the final product is right is the product of the probabilities P1, P2 and P3 that each of the three operations is done right, assuming that they are completely independent of one another. If my boring is always 100% right but my turning and parting are only hitting 90%, I'm at 81% overall. There's no point looking to my borer for improvements, I need to talk to my turner and my parter to see whether one of them can get up to 100% or both can get to about 95%, or some other arrangement which gets the product of their two outputs up to 90%.
On the other hand, I could find that the boring is 90%, the turning is 90% and the parting off is 100%, but from inspection I find that the turning is always offset from the bore. That makes the ratio between turning and boring 1:1 but the turning is dependent on the boring. My success rate is 90% because everything with a good bore also has a good OD.
gbj_tester-
The quality targets are KPIs for an Engineering manufacturer. There are three shops (Weld, Paint and Assembly) to which each is allocated one of the sub targets, A, B and C. The overall target and the result of the formula is the overall plant result. I'm not convinced the formula is the best way to calculate an overall result, but it's the company's global standard and little me isn't going to change it. All the percentages represent the proportion of products that go through their respective shops without being repaired, eg correct first time. Each year we study previous results and derive the ratios, as they are easy for everyone to understand relative performance and allocation of targets between each shop.
Hope is crystal now!
efb
Perhaps percentages confuse the issue? For this calculation we treat as normal numbers.
Example calculation
Sub targets = 70%, 80%, 90%
Total target = 50.4%
As 50.4 = (70*80*90)/10000
You've got me wondering if my ratio calculations are wrong.
A+B+C can be anything between 0 and 300.
Thank you for your help!