Written in response to this post on the DEN (broken link removed). The responses on this topic show the strength of the DEN.
1) thoughtful responses that should help the person posting the original message
2) thoughtful responses that are of interest to many of us
3) the chance to explore concepts in some greater depth than we may otherwise
Relating to the 3rd item in my list I would like to explore part of Myron’s response. “Loss functions are highly personal. To ascribe a loss function to society requires plenty of hutzpah!” I think, the Taguchi Loss Function is meant to show the loss to society as a whole. My understanding, is that the Taguchi Loss Function is meant to show the overall quantifiable loss to society.
I must say that while viewing the overall loss to society is worthwhile, I think it is often more useful to see (or think of) the losses to each of the various parties. I believe this for the following 2 reasons.
First, to ascribe the loss to society, as Myron notes, requires plenty of chutzpah and I think is often going to lead to attempts to quantify impacts that are difficult to quantify. My understanding is that the Taguchi Loss Function limits the losses to quantifiable losses. If the losses are actually quantified then it should be a simple matter to include whatever losses you choose to get a picture of the factors you wish to focus on, which is good.
However, in practice, I have seen the concept of the Taguchi Loss Function used quite a bit. I have never actually seen any losses quantified and totaled and shown on a graph. I think focusing specifically on who suffers a loss and what that loss could be, can help. I think actually quantifying the losses to society can be daunting. So, while I see the value in framing the concept that way I think to actually get the losses quantified you are best served by starting with those closest to the process and then adding additional loses to those results.
Second, if you attempt to use the concept to help you manage (as a guide in decision making) the impacts to society are a factor, but, I think the loss to your company, the customer and perhaps the end user are most important. A negative impact to society at large is not going to have the same impact to a decision maker as the same negative impact to the customer. The decision maker will likely be willing to invest more to reduce the loss to a customer than to society at large (and that seems logical and sensible to me).
I believe the Taguchi Loss Function is a great conceptual model. I also think it is important to understand that the shape of a loss function in any situation depends on that specific situation. A parabola does a good job of illustrating the concept that loss is normally not binary and often increases somewhat slowly very close to the optimal result and more dramatically as the deviance from the optimal result increases. The loss is often not equal on either side of the optimal result in which case a parabola would not be the best model.
The important factor when making a decision, in a specific case, is to look at the losses that actually exist for that case. And, in my opinion, knowing where the loss is felt matters – so only viewing the overall loss to society is not sufficient. However, this concept is not part of the Taguchi Loss Function, but rather, is my opinion of how the concept can be applied most effectively. And while the concept of the Taguchi Loss function does a great job of showing why specification limits are not sufficient to good management, it is true that is some situations the loss can be pretty much binary, good (no loss) or bad (100% loss) with little, or no, “grey area.”