Last night we discussed the Taguchi Loss Function and how Taguchi methods are more concerned with hitting the target compared to more traditional methods that often focus on keeping our data between the upper and lower specification limits.

Cpm

Staying with this theme I now want to introduce Taguchi’s version of Cp and Cpk which we call Cpm. Truth be told I don’t know where the “m” comes from. Perhaps it has ties to a Japanese word. I will default to someone like Jon Miller who knows a bit more Japanese than I. Also, if someone else knows where the “m” comes from please do share!

What I do know is why we actually prefer Cpm to Cpk in certain situations. It all has to do with the relationship between our “target” and the specification limits.

Example of when to use Cpm

For example, let’s say we are machining a part with a LSL (lower spec limit) of 10 mm and a USL (upper spec limit) of 20 mm. Let’s also assume our customer asks us to produce the part to 18 mm instead of the more typical 15 mm (dead center).

In other words, instead of being right between the LSL and USL our customer wants us to bias the dimension more towards the USL. While this biasing may not be the norm, it does occur. When I teach Cpm and ask a room of 25 for examples of where they have seen a bias towards one spec limit I normally get several examples. If you have an example please leave us a comment.

Cpk Makes no Sense

In this situation using Cpk makes little sense since we are purposely shifting the mean of our process a bit towards the upper specification limit per our customers request. In fact, assuming we are successful and are able to consistently produce a machined part of 18 mm Cpk would penalize us since the process is “shifted.”

A better method, in this example, would be to use Cpm which uses the “target value” in its calculation. In other words we will not be penalized for not being dead center between the upper and lower specification limit.

Math Geek Fix

For those interested in the math, the key difference between Cpm and Cpk has to do with the the way standard deviation is calculated. The traditional Cpk standard deviation is calculated by comparing each data point to the mean of the process. When calculating Cpm we use a different method to calculate the standard deviation. Instead of comparing the data points to the mean of the process we compare it to the target value.

Note that if the target for our process is dead centered between the LSL and USL Cpm and Cpk will be almost identical.

Well that is Cpm in a nutshell. I can’t promise a third straight day of Taguchi fun… then again you never can tell. So please stay tuned!

Subscribe to LSS Academy

If you enjoyed this article please consider subscribing to our full feed RSS. You can also subscribe by email and have new articles sent directly to your inbox.

Saying the words “Genichi Taguchi” to a hard core “western statistician” may get you some dirty looks. Actually, some of these crazy statisticians may want to strike you for saying this person’s name. Why the hate you may ask?  Good question.

Let me give you my take on it. Genichi Taguchi is a Japanese engineer and (close your eyes western stats geeks) statistician.

Hard core statistics nerds (most of whom never actually make it to the gemba) will tell you how Mr. Taguchi’s methods break all kinds of rules. They will spout out words like orthogonality, confounding, and all kinds of other gibberish in hopes you will turn your back on Taguchi methods.

Ignore them!

Fear not friends… those statistics friends of ours should be ignored and allowed to study their monitors all day long leaving everyone else alone. I am hear to tell you that Taguchi methods rock and I have used them many, many times successfully. My favorite Taguchi DOE is the L18. I will blog more about this in the future.

Tonight I want to introduce a key concept Taguchi teaches known as the “Loss Function.” It is at the core of all Taguchi methods and must be understood.

Traditional Bell Curve

Let’s start with our traditional “bell curve” approach to defects. Typically we see people draw in upper and lower specification limits (customer requirements). We then see a bell curve drawn in between these specification limits. If a data point falls outside a spec limit we have a defect. If all the data points are between the spec limits there are no defects. Simple as that, right?

Sort of.

Brain Surgeon Final Exams

Say you need to have brain surgery (I pray this never happens by the way). With something so serious it’s safe to assume you would want a top notch surgeon, right? Of course you would. But guess how surgeons get the right to slice into your head? They take exams, bunches of them, in medical school.

Imagine two nice fellows, Bob and Ted, are going through brain surgeon school together. Now imagine they are sitting for their FINAL exam. If they pass this exam they have the right to slice your head open.  After much study Bob and Ted take their exams.

Bob scores a 61% and Ted scores a 59%. Bob is celebrating and sharpening his scalpel as he “passed” the exam. Ted, poor guy, flunked and is looking into this new methodology called MVT as he hears it is replacing Six Sigma… this medical school stuff just isn’t working out for old Ted.

Is There Really a Difference?

But, really, is there really much difference between Bob’s knowledge and Ted’s knowledge? Not likely. Instead, what probably happened is Bob guessed right a few more times than Ted and earned the right to be a brain surgeon. Since his test score was “between” specification limits he passed. And since Ted’s score was outside the spec limit he is sent packing.

Enter the Loss Function

Genichi Taguchi realized this and hated it. So, he decided to turn that bell curve on its head – literally.

Taguchi said that having specification limits was all well and good. But what he wanted people focusing on was the “target” value. He stated that the further we drift away from the target value the more it costs the company. We want to aim for the target while doing all we can to reduce variation. The spec limits don’t get too much of our focus since we only want to nail that target and don’t stop until this is our reality.

This is not contradictory to what Six Sigma teaches. Six Sigma also aims to reduce variation while centering our process about the target. But if a Six Sigma practitioner ever becomes disillusioned with the fact that simply staying between the specifications limits is our goal explain the story of Bob the brain surgeon with the very expensive malpractice premium.

I will write more on Taguchi methods in the future. There are some really slick ideas I want to share.

Subscribe to LSS Academy

If you enjoyed this article please consider subscribing to our full feed RSS. You can also subscribe by email and have new articles sent directly to your inbox.