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%" :confused: .

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 :rolleyes: ), so I'd sure like to have any responses toned down to an elementary level.

Bill

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...

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

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.

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

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.

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?

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

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.

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 :rolleyes: . 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 :bonk: ).

Bill

Dave Strouse,

I calculated using Excel (I don't have Minitab), and in my haste, made a mistake that just happened to show the same 98% Bill cited :o . Nevertheless, you don't need Minitab to know the process isn't capable! (NOTE: I'm curious about a shape parameter of 16.71? I did a histogram of the data and it looked fairly normal to me. Beta (shape) for normal is around 3.5). 16.71 is pretty wild.

Bill,

A 50% confidence level is nonsense (most tables go no lower than 90%) and only shows that the people presenting the data lack an understanding of the statistical tools they're using.

Steve Prevette made a good common sense reply.

[QUOTE=Rob Nix]A 50% confidence level is nonsense (most tables go no lower than 90%) and only shows that the people presenting the data lack an understanding of the statistical tools they're using.
[QUOTE]
It finally came to me - the 50% confidence level is basically the median. Half the data will be above it, half below it. Half the time I am better than X and half the time I am worse than X.

And depending on how skewed the distribution is you fit, if the fit is based upon the average and perhaps the standard deviation, you could conceivably drive the median of the "distribution" to be about wherever you want it.

Bill -

I looked at your data again.I had entered it in by columns.Was this how it was collected? If it was, it raises some more questions. If it was not, disregard below. A I-MR chart shows that the last 15 points are hugging the center. Was there a change in metrology? A change in process?

The capability is still not great, but certainly better on the last 25 only. And the 25 cutoff was arbitrary. I think the last 15 would be better yet on capability, but I think you need to understand the special cause in the range chart and the individuals. Could be that you can meet the spec with minor changes. This might be why the customer thinks it's OK. However,I don't understand at allwhat they have told you. One of my graduate professors used to say" If you only want 50% confidence,don't bother looking at the data nor running experiments, Just flip a coin!" ;)

For Rob (and myself being curious) I also generated lots of random numbers from the Weibull distribution shown as best fit to all the data.It's pretty heavy tailed left. But it's way to early to even try to fit any model until we understand the data and why the process appears so bad.Is it real?Is it metrology or some time factor in the process.

Trying to (really) attach file from last post.I hope it works!

Trying to (really) attach file from last post.I hope it works!

I guess Dave and I were performing the same thing :)
Here is my analysis reports on the data. I will join later this evening in the discussions.
:read:
Got Back after a long day.

I dont know the reason why your customer used Weibull. I guess they are assuming that the data with onesided Specification as Non-Normal and trying to fit Weibull.I think Weibull usage in this application is not appropriate.

I looked at the data. Iam not convinced that the data as is can be analyzed as Normal due the skewness -0.837 (even though the “p” value is 0.095)

After verifying through 95%CI Normal Plot, I decided to perform another analysis excluding the point #8. (Iam treating this point as an Outlier). The user should find if any special cause is related to this observation before discarding the data point.

After excluding the outlier, the data fits into a much better distribution with a “p” value of 0.359, Skewness is now 0.134 ( as it is gets closer to 0, the distribution is more symmetrical).

I have performed a 95% CI with and without exclusion.(See attachment2)

My interpretation would be: Example for the Strength2 i.e Outlier excluded data is,
With No change to process and variation (statistically) if you pick 100 samples and test them for the strength there is a possibility that 1 Sample can be lower than 12.116kN and 5 Samples more than 15.361
Later I went back to Capability Calculation to verify which value would give you a higher capability.
With the current process, lack of specification, 11.3kN as min strength will provide acceptable Capability>1.3. Also, consider if there is need to conduct R & R for Destructive testing. We have not considered the measurement system variation yet.

Govind.

Steve
If your statement is correct, I believe you have compounded my "confusion". If I understand correctly, you're statement tells me that 50% of the time I will be above the 13.2 minimum at a 98% reliability level - and 50% of the time I will be below the 13.2 minimum at a 98% reliability level. So, my (potential) customer is telling me that he will (graciously) accept my process which is producing over 50% scrap. I've got to agree with Rob that a 50% confidence level doesn't make sense.

Dave & Govind
I couldn't view Dave's attachment but will assume (my favorite word :rolleyes: ) it is similar to Govind's. I did the same in Minitab and got the same charts. Thanks for the correlation so I at least know I'm looking at the same things you guys are trying to help me understand.

Dave
I'm not sure if these parts were tested in order or just thrown into a pile and randomly tested (this is a fellow engineer's project who knows less about reliability than I do). I'm also not sure about the homogeneity of the samples - meaning - I don't know if there is some "burnoff" at the dipwell before the aluminum gets shot into the die, and as the upper layer of molten metal is used up, if the metal chemistry then becomes more consistent. I have suggested to my peer that he do a "time ordered" approach for more insight into our process and he's all for it.

Bill

I'm not sure if these parts were tested in order or just thrown into a pile and randomly tested (this is a fellow engineer's project who knows less about reliability than I do). I'm also not sure about the homogeneity of the samples - meaning - I don't know if there is some "burnoff" at the dipwell before the aluminum gets shot into the die, and as the upper layer of molten metal is used up, if the metal chemistry then becomes more consistent. I have suggested to my peer that he do a "time ordered" approach for more insight into our process and he's all for it.Bill

Bill,

When I first looked at Govind's analysis I had planned on making some follow up comments. Now that you have stated that you are not sure if the data is time ordered than you have a problem since the control chart is only used for time ordered data.

Assuming the way Govind entered the data is correct, I was going to make the following comments (keep in mind that they may not be valid now).

1. The histogram looks two humped which can be an indication of multiple process data combined together.

2. A look at the raw data, again assuming time ordered, shows that the first 8 points fluctuated above and below your minimum spec. It almost looks like the process was being changed to get the product to meet the spec. If true than that data is when the process was obviously unstable and should be excluded from your control chart. That would also explain the two humped histogram. I did not run a control chart with those excluded so maybe Govind can help.

3. The moving range chart had out of control points for the first 8 data points. I have been taught that the range chart must be in control before the control limits can be established since out of control points on the range chart are an indication of an unstable process.

4. Is the data only for a special production run for the customer or is it the data for what was sent to the customer that is part of a larger production run? If it is the latter than you could be "cherry picking" the product for your customer that meets the spec and it will not tell you anything about the capability of your process.

It has been some time since I thought this much about SPC so anyone can feel free to take shots out my analysis.

Bill Pflanz

Steve
If your statement is correct, I believe you have compounded my "confusion". If I understand correctly, you're statement tells me that 50% of the time I will be above the 13.2 minimum at a 98% reliability level - and 50% of the time I will be below the 13.2 minimum at a 98% reliability level. So, my (potential) customer is telling me that he will (graciously) accept my process which is producing over 50% scrap. I've got to agree with Rob that a 50% confidence level doesn't make sense.

Bill

Not 50% scrap. Let us take the "usual" 95% confidence that no more than 5% of the parts are defective. I take a sample of 59 and none are defective. That means that there is 95% probability that the proportion defective in the population is 5% or less. That means I am quite sure that I will not see a defect rate of more than 5% from this population.

If I have 50% confidence that the defect rate is 2% or less, that means (following a sample of whatever size gives you that) that there is a 50% probability that the population proportion defective is less than 2%, and a 50% probability it is more than 2%.

Another way of looking at it is that if I took 20 lots and sampled them, I would expect that 10 would have a proportion defective of less than 2%, and 10 would have a proportion defective of more than 2%.

Bill,

When I first looked at Govind's analysis I had planned on making some follow up comments. Now that you have stated that you are not sure if the data is time ordered than you have a problem since the control chart is only used for time ordered data.

Assuming the way Govind entered the data is correct, I was going to make the following comments (keep in mind that they may not be valid now).

1. The histogram looks two humped which can be an indication of multiple process data combined together.

2. A look at the raw data, again assuming time ordered, shows that the first 8 points fluctuated above and below your minimum spec. It almost looks like the process was being changed to get the product to meet the spec. If true than that data is when the process was obviously unstable and should be excluded from your control chart. That would also explain the two humped histogram. I did not run a control chart with those excluded so maybe Govind can help.

Bill Pflanz

Bill,
1.I think it is very difficult to judge the distribution as bimodal with so little data.I would say a collection of 100 points is decent enough to talk about distribution mode.

2.Initially row 8, 35 in the x chart and 5,6,8 in MR chart were identified as a points that violate the rules.
First iteration, I tried removing 8,35: all points met X chart but points 5,6 violated in MR.
Next iteration, I removed 5,6.
1,2,14 and 20 in X chart and 15 in MR is violating.
This is too many points to remove. After, I remove all these points,the results will be misleading.
I dont go more than 2 iterations. If I donot see all points under control after 2 iterations,I discard the data and start again.
I guess next time Bill Ryan collects time sequence data with more points, we can offer to provide some statistical assitance putting all our brains together.
Govind.

:thanks: Thanks again guys. As it happens we are running another sampling next week. I'll keep you posted.

Steve
Thank you for the explanation. I have always had difficulty grasping some concepts related to testing and confidence level. Sometimes things click and other times it's like I'm in a fog :bonk:

Bill

Bill,
1.I think it is very difficult to judge the distribution as bimodal with so little data.I would say a collection of 100 points is decent enough to talk about distribution mode.

I agree about the small amount of data to make that decision. My next step is to look at the raw data. Using your control chart and looking at the pattern of data in the first 8 samples is additional reason to question if bimodal. My final step would be to talk to operations about what was going on at that time. Relying totally on statistical analysis is a risky thing to do.

This is too many points to remove. After, I remove all these points,the results will be misleading.
I dont go more than 2 iterations. If I donot see all points under control after 2 iterations,I discard the data and start again.
I guess next time Bill Ryan collects time sequence data with more points, we can offer to provide some statistical assitance putting all our brains together.
Govind.

I also hesitate when I remove any data from the analysis. There should be a reason (bad test result, incorrect reading etc.) for removing the data not just that it is an outlier. Without a specific reason for removing it then you could be removing data that is part of the process. I only recommended removing the first 8 data points if they were collected when the process was being brought into a stable process. I also will be interested in any new data that Bill collects since we are assuming a lot with the current analyses.

We have two different discussions going on about one question since there has also been comments on confidence levels. They are not necessarily related to each other so I hope Bill is not getting confused.

Not to add confusion but...
(the other) Bill

Once again I'd like to thank all of you for the replies :thanks: .

As it turns out, management decided to have the customer find someone else to make the part, and they have done so. We never did the "next run" so I have no new data to contribute. On one hand, I'm sorry as I feel I was just on the cusp of grasping a couple of concepts that I've had trouble with in the past. On the other, I think everyone here is breathing a little easier as this part looked like it might have been a loser for us.

Oh well, on to the next part (which I'm sure is full of some other "opportunities" :rolleyes: ). Just wanted to put some "closure" to this and not leave anyone hanging.

There are some companies that use the Weibull distribution to describe the distribution of tensile strength; for example, in tensile testing of aluminum castings.

But they have tons of data and use the Weibull because it best describes the process.

The key, I think, is tons of data.