Yes, I know specification limits should be set and agreed to with the customer. But sometimes a stake needs to be put in the ground to get people talking.

Minitab is happy to report the Cpk values if I supply a target and specifications, is there a way to supply a Cpk value and have it give me the specificaitons that result in that Cpk? Or is there another way to do this? I have been manualy recursing to get this info (Give specs obtain Cpk, adjust specs get new Cpk, continue until converged), but it seems that there should be a quicker way.

Thanks for any help.

... But sometimes a stake needs to be put in the ground...

Aim higher! The stake belongs above the navel and below the chin.

I've looked for the same thing with no luck. I use the eyeball method.

One other question I meant to ask the gurus. When I use equal sided specifications (High-target = target-minimum), vary the size of the range and plot the resulting Cpm values vs the width of the specification I get what looks like a very straight line. Is this line really straight in all cases? Can I just get two values draw a straight line and obtain my specs to achieve a given Cpm? Is the same true for Cpk? Does it matter if the data is normal or not?

Since Cpk is the smaller of

Cpl = (X-bar - LSL) / 3s
Cpu = (USL - X-bar) / 3s

you could work the algebra backwards to solve for USL & LSL.

I get the spec limits at (X-bar) +/- (3*s*Cpk).

Assuming you know X-bar and s for your process, you can just plug in the numbers. Note that only one of the spec limits must be at the numbers listed above. The other one could be anywhere farther out and you would still get the same Cpk


Added after seeing the second post:

As for plotting a straight line, it should work. I wouldn't have thought to do it that way, but it makes sense after a little thought. If you plot Cpk along the x axis and one of the spec limits along the y axis, then the equation above looks suspisciously like

USL = (X-bar) + (3*s) * Cpk
y = b + m * x

So your graph should be a straight line with a slope m = 3*s and a y-intercept of b = (X-bar)!


Tim F

Yes, I know specification limits should be set and agreed to with the customer. But sometimes a stake needs to be put in the ground to get people talking.

Minitab is happy to report the Cpk values if I supply a target and specifications, is there a way to supply a Cpk value and have it give me the specificaitons that result in that Cpk? Or is there another way to do this? I have been manualy recursing to get this info (Give specs obtain Cpk, adjust specs get new Cpk, continue until converged), but it seems that there should be a quicker way.

Thanks for any help.

First, you can always calculate Cpk in Excel and use the "Solver" function (Tools-->Solver) to determine the specification limits.

Second, I'm not sure what you are looking to prove through this exercise. What will happen is that the specification limits required to meet the desired Cpk may end up so large that you could drive a Mack truck through them.

Out of curiosity, what are you looking to prove?

Wayne

Not really trying to "prove" anything. Have a new product rolling out and am in the process of working up specifications. The customer is requesting 6 sigma level of performance, but does not seem to be willing to give a specification range for the parameters of interest. For example after several conversations about a key dimension the response on the specifications was we need the dimension to be x inches. No range for acceptance just the center point. So my question is in this case what would you propose for a specification and tolerances? X +/- 0.5%, 1.0%, etc? It turns out my equipment will operate at 6 sigma level at +/- 0.35%. So lacking any other information from the customer and using my best guess as to whether or not this will meet there needs I plan on proposing this as the specification. If nothing else I hope to get some type of dialog started with the customer. If they suggest a wider range great, if they want a narrower spec, I already have some idea what that will cost me in productivity, scrap, etc. As I indicated in the first post this is just a stake in the ground to try and get a process that is stalled, not on our end, rolling again..

The customer is requesting 6 sigma level of performance, but does not seem to be willing to give a specification range for the parameters of interest. For example after several conversations about a key dimension the response on the specifications was we need the dimension to be x inches. No range for acceptance just the center point. So my question is in this case what would you propose for a specification and tolerances?

I had a feeling this was the direction you were heading but just wanted to be sure. Something to keep in mind is that Cpk is measurement of a process against specification limits. Process capability measurements don't necessarily equate into a "quality" product.

Let's take a process that we'll assume is in control but has a poor Cpk index when compared to a tolerance of +/- 0.020". We can increase the Cpk value to 1.66 if we increase the tolerance to +/- 0.100".

Now we take a part (B) which mates to the first part (A). Part "A" is at X+0.050" and Part "B" is at X-0.050". The stackup yields a gap of 0.100". Both parts are clearly acceptable when checked individually, but when used together the gap would be 0.060" greater than the narrower tolerance even though the narrower tolerance yields a lower Cpk.

Tolerances shouldn't be decided solely based upon some index without regards to other factors involved. Just recently I was involved in a similar discussion with our engineering group regarding a new product and their focus on a "good" Cpk versus what truly makes sense.

For your particular application it may work to go the route of setting tolerance limits based on the ability to achieve a certain Cpk value, but that isn't always the case.

Just food for thought.

Wayne

Thanks for the insite. In this case we are not talking about parts that mate together, but your point is well made.

First, you can always calculate Cpk in Excel and use the "Solver" function (Tools-->Solver) to determine the specification limits.
Wayne
I tend to be a fan of Excel's "solver" and have use it for everything up to non-linear least-squares curve fitting. It is a great tool, but I do have one concern in this case. Cpk can be adjusted by moving either spec limit. It is not clear whether Excel would adjust the upper limit, the lower limit, or some of each in this case. The danger is that Excel will find one of many possible solutions and you may not think of that as you interpret the results.

Since the solution is a straight line in this case, it is quite easy to simply rearrange the equation and plug in the specific numbers.


Tim F

I have a spec for a gage here infront of me with a +0 - .000005 tolerance.

The designers I deal with think .0001 is a real number.

A friend here tried to explain in a top level meeting, and said. "Do you know what .0001 is [mr. designer]? - It's the smell left on your finger after you wipe your a**."

I laughed so hard I nearly wet myself.

Remember that Cpk is a "snapshot" of the process. Unless your sigma reflects an estimate of long term variability, your Cpk and Cpm will jump around based on sampling error used to estimate the standard deviation.

Agree with Statistical Steven, I must add the dependence to the sample size of the Cp index estimate, that topic hasn't be touched in this post (altho is part of the sampling error) and as I stated before it depends on the sample size.