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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-
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
So if the welders are getting 90% of their jobs right first time and the painters are only getting 40% right first time, your allocation of targets using the same ratio as they achieved last year might mean the welders have to work their butts off get up to 95% while the painters can keep slacking off and still hit their new 42.2% target.
If I understand correctly, the targets should not be success rate, they should be error rate, and they should be a proportion of the errors, not a proportion of the total production. Now the welders just have to halve their error rate from 10% to 5% to earn the same bonuses which the lazy good-for-nothing paint shop won't get until they too have halved their error rate from 60% to 30% :-)
gbj_tester
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=kABC
will 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.