Hi, All!
I got a question about setting up and fitting a Taguchi Loss Function. The question was around using it in the context of control limits or within a control chart.
Thoughts?
M
As far as I remember, the Taguchi loss function is a way to put a heavier weight on observations as you got closer to the limit. The idea is that stuff closer to the mean (or the bound side for a one sided limit) should be worth more/cost less/be of a higher quality than stuff closer to the limit. This is different from the typical all or none approach (in spec = good, oos = bad). I've seen it applied to capability indices and as a methodology for quantifying consumer/producer risk, but not in the context of control, which is almost always distributionally based. I suppose you could come up with arbitrary rules as to when something is out of control. In simple cases you could probably even work on the distribution of the loss function (e.g., squared loss would follow a chi-square, I believe).
Don
I agree with Don McCormack. We usually used the Taguchi Loss function in the context of capability analysis, not process stability. It's a pretty simple construct:
https://en.wikipedia.org/wiki/Taguchi_loss_function
Essentially, the default function is a 'loss to society' (in Taguchi speak) in $$$$$ on the y axis, and deviation from aim on the x axis. Default construct for the parabolic curve is in the reference above. Our standard practice was to use the material cost of scrap for lost batch (L), then just solve for k. Once you have the function for the CTQ characteristic, now you can play what if scenarios for variation reduction efforts by showing the delta in 'loss to society'.
The shape of the curve has been open for public debate forever...'is a parabola 'right'?' etc. But the idea has some intuitive merit so we usually just used the standard formula for consistency across processes/products within an enterprise.
