Weibull vs. Gaussian on something that is not a durability or life cycle test

[Bill Ryan - 2007]

We are in the process of launching a new part - a latch. There are strength requirements spelled out on the part drawing. This is an ongoing "in-process" check as defined on the drawing. We've performed some tensile/compression testing and the results "pass" normality tests. In order to meet a Cpk of 1.67 (our minimum requirement to take the job) we need to move the lower specification.

Our customer has come back to us and said the specification is fine because our parts meet a 1.00/1.33 Cpk (unacceptable to us). They have further "proved" their point by performing Weibull analysis and stating the lower spec. limit doesn't need to be adjusted because "the variable data meets the targets with a minimum probability level of 98% at a confidence level of 50%" .

Can anyone explain to me why they would be using Weibull analysis on something that is not a durability or life cycle test but rather a static tensile/compression test? And - why a confidence level of only 50% would be acceptable? I'm just fearful that we are giving ourselves a tremendous opportunity to fail. Please understand, I have a pretty superficial understanding of reliability statistics (for that matter, most statistics ), so I'd sure like to have any responses toned down to an elementary level.

Bill

 

[Al Dyer]

I believe this would be a poser for Atul or one of the other "Gurus" in that area. My knowledge is not deep enough to answer in an intelligable manner.

Al...

 

[Bill Ryan - 2007]

That's OK Al. I'm not even sure the questions make sense to "someone in the know".

 

[Rob Nix]

Bill,

I want to provide an in depth response but cannot for the next few days. My short answer is to agree with you that Weibull is not the appropriate distribution model. I'd like to see some of your data and spec limits, and their rationale for using Weibull.

More to come.

 

[Bill Ryan - 2007]

The specification is 13.2 kN minimum. Here are 35 data points from a sample run:

12.4 14.3 14.1 13.5
12.8 14.7 14.4 13.6
14.1 14.5 14.6 13.8
14.7 15.7 13.8 14.0
12.7 13.4 13.8 14.3
15.7 13.7 14.3
12.5 13.5 14.7
10.7 13.4 13.6
13.8 15.1 14.4
13.7 15.5 13.7

These numbers work out to a Mean of 13.93; St. Dev. of 0.98; a Lower Control Limit (3s) of 11.00; and a Pp (lower) of 0.25.

The test for normality yields an Anderson-Darling value of 0.625 and a p-Value of 0.095 (95% confidence level). All these numbers tell me we cannot produce a "zero defects" part for this customer (with the current material and process). They also had some parts from the run and came up with their Weibull statistics stating that at a 50% confidence level they show 98% reliability with the 13.2 specification (which they had labelled as "Time").

Even if their numbers are higher than ours (testing variability or perhaps those parts actually were "better"), doesn't their 98% reliability translate to 2% of the parts failing the minimum specification (200,000 ppm)?

Bill

 

[Rob Nix]

Your raw data shows 86% (30 of 35) within spec.

The area under the normal curve based on your mean and std. dev. is 77%.

Either way you look at it, it is clearly not capable.

The Weibull function shows 98% (I checked and got the same) but it is pretty forgiving of fliers (like your 10.7 reading). However, remember that percentage represents the ESTIMATED proportion of parts making it to 13.2 kN. (That's why I think it is not the best function).

The original use for the Weibull function (1939) was for strength calculations. It was debated by many. The rationale supporting it was this: It is related to time in that you are finding out HOW LONG, under steadily increasing strain, the part will go before failing (and there is always a failure, or defect, that triggers the yield/break event).

Most books today show the uses for Weibull include strength tests and time to failure (or time to repair). However the best use of the statistic is for time related studies (reliability over time like MTBF or MTTR), not strength, IMO.

I like statistics I can visualize and get my arms around. I don't use Weibull even when doing R&M studies. I use MTBF, MTTR, failure rate, and availability.

You could try doing a Weibull plot of your data just to visualize it better.

I'm rambling, but I hope some of this helps. It's been 12 years since I did Tensile Strength/Yield Capability Studies.

 

[Dave Strouse]

How?

Rob , you said -
"The Weibull function shows 98% (I checked and got the same) but it is pretty forgiving of fliers (like your 10.7 reading). However, remember that percentage represents the ESTIMATED proportion of parts making it to 13.2 kN. (That's why I think it is not the best function).
"
How did you do this?

I used MINITAB software and non-normal capability analysis and also normal. Either way the PPM predicted was greater than 200K, so I think the Weibull vs Normal model debate does not make much difference. With these small samples it would be hard to tell.

MINITAB shows a probability plot indicating the data fit Weibull with shape of 16.71 and scale 14.35. In no way then will the 13.2 spec be capable.

Weibull is certainlly an approbriate model for stress in many cases. In fact I believe this was the original paper that Weibull published. This process,however ;is so bad to the spec that something must be done to give the customer good parts.

I don't where this 2% number comes from.Can you explain what you are doing?

 

[Steve Prevette]

Methinks this is why Dr. Deming lashed out against distribution fitting. You clearly have parts in the set of 35 that didn't make the specification. They were bad parts, and I assume had to be scrapped or reworked (or force fit into the application with a "persuader"). I am sure I could find some distribution that would paint a rosy picture.

Seems strange that you are the supplier and believe they are "bad" and the customer thinks they are "good". It does seem fishy, and it does make one wonder if the specification does have any meaning to them.

I suppose, in an ideal world, I would work the system so the parts did meet specification anyway. In theory, that would delight the customer. But I am reminded of the story of the well-meaning hospital stock room person who ordered catheters that were cheaper and sharper than those currently in use - you would think sharper would be better, right? Nope, caused lots of problems to the doctors due to the unexpected change. So I would still pursue trying to understand the customer's "true" needs.

Steve Prevette
ASQ CQE

 

[Darius]

As Steve said

Seems strange that you are the supplier and believe they are "bad" and the customer thinks they are "good". It does seem fishy, and it does make one wonder if the specification does have any meaning to them.

I agree that there is no point of discusion about that your product can not be good for the customer with the current lower spec.

I tink you have 2 ways (because for the customer the product looks OK)
* change the spec to a lower value (assuring him a cpk of 1.66).
* make an agreement about the ppk that you are going to produce (ppk of 0.28), wich states it as an accepted quality.

 

[Bill Ryan - 2007]

Thanks for the replies gang. A bit more of "the rest of the story"......

The specification is from an FMVSS standard so I'm not too optimistic about getting it changed . A competitor was making this part (for about 4 production runs) and decided to "chuck it". Their process was, also, not capable. We do have a couple of options to pursue with our processing - one being to offer it in a different alloy (but that would affect piece price a bit).

Regardless of the numbers I posted, I don't understand why you would use a 50% confidence level and be happy with any reliability number. In other words, couldn't I use a 25% confidence level to get, say, a 99.999% reliability? That doesn't sound very "impressive" to me unless I'm thinking entirely incorrectly (which is not that uncommon ).

Bill