Ppk of non-normal bounded proccess, one sided specification

D

davis007

#1
We have a new customer that has asked for our specifications to be updated to include a measurement of the leakage rate of our parts. The parts open and close and the spec is related to how well sealed they are when closed. To perform the test a sealed part is placed in a chamber that is rapidly evacuated to some negative pressure, after a given period of time the pressure is recorded, if the parts leak the pressure in the chamber will rise. The increase in chamber pressure/time is the "leak" rate of the part.

The customer is allowing us to set the specification and we have agreed to set it such that we will achieve a Cpk (what Minitab reports as Ppk) of 1.33. However, I have two issues. First the possible measurements for this leak rate, barring equipment failure, are bounded, a perfect seal would give a leak rate of 0 but less than perfect seals always result in a positive leak rate. How do get Minitab to handle a one sided specification?

Second the data is not normally distributed, mostly due to the fact that the data is bounded and the target is the lower bound. I have found that a 3 parameter Weibull fits the data very nicely and sort of solves the issue of the bounded data. However, when I run the non-normal capability analysis with a spec of 0 (the boundary) and any upper spec higher than ~164 I always get the same Ppk value.

Any ideas what I can do? Is there a limit to the achievable Ppk for a Weibull distributed process?
 
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D

davis007

#2
Re: Ppk of non-normal bounded proccess

Well I answered both questions myself.

First, If you run capabiliyt analysis and NOT the capability six pack you can indicate if the limits are specs OR boundaries.

Second, Now that I am running with a boundary understood by Minitab the Ppk value is dependant on the upper specification, as I was thought it should.
 
D

duecesevenOS - 2009

#3
The customer is allowing us to set the specification and we have agreed to set it such that we will achieve a Cpk (what Minitab reports as Ppk) of 1.33. However, I have two issues. First the possible measurements for this leak rate, barring equipment failure, are bounded, a perfect seal would give a leak rate of 0 but less than perfect seals always result in a positive leak rate. How do get Minitab to handle a one sided specification?
Careful with this. Cpk and Ppk are two different things. Minitab can show both of them. I'm definately not the expert on this but one of the reasons I started looking on the cove was to get clarification on the subject. Take a look at the sticky topic in this group, its very long but the differences between the two numbers can be a heated topic (evidently). ;)

I'm not sure from the information you gave but are saying that these parts are going to be 100% inspected? If so a lot of the differences between the Cpk and Ppk go away (I think). This is a direct quote from another thread but I can not remember where I found it. This kind of explains everything for me.

Cp - process CAPABILITY if process was centered and fully stable - the very best the process could be - assumes process is stable and centered on target - no subsample to subsample variation

Cpk - process CAPABILITY if instability were removed - assumes process is not necessarily centered - assumes process is fully stable - no subsample to subsample variation

Pp - process PERFORMANCE if centered on target - assumes process is centered on target but uses the actual process variation, including any instability (subsample to subsample variation)

Ppk - the actual process PERFORMANCE - including both lack of center variation and instability (subsample to subsample variation)

By comparing these four indices to each other you can understand the extent how off-target and unstable the process is, although it would be easier to just give the mean & standard deviation of the process and then visually compare it to the specs.
 
D

davis007

#4
Thanks for the reminder.

In Minitab the formulas for Ppk and Cpk are the same except:

For Ppk Minitab uses the overall standard deviation of the data, and for Cpk Minitab uses the "pooled" standard deviation (this defaults to the same when the sub group size is 1.

In practice what I care about is the long-term fraction of product that is within the specification limit. This is across lots and campaigns. Thus the measure of interest is what is reported by Minitab as Ppk.

What is reported by Minitab as Cpk is useful for me to understand how the process could perform if you could eliminate subgroup-to-subgroup variability.
 
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