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

R

Rob Nix

#11
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 :eek: . 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.
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#12
Rob Nix said:
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.
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.
 
D

Dave Strouse

#13
How bout another look?

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.
 

Govind

Super Moderator
Staff member
Super Moderator
#15
Dave Strouse said:
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.
 
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B

Bill Ryan - 2007

#16
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
 
B

Bill Pflanz

#17
Dave said:
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
 
Last edited by a moderator:

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#18
Bill Ryan said:
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%.
 

Govind

Super Moderator
Staff member
Super Moderator
#19
Bill Pflanz said:
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.
 
B

Bill Ryan - 2007

#20
: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
 
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