If we have a capability problem and we need to do a capability study, can we get an accurate picture of taking 6 pieces from one lot (that's all we have) and 6 pieces of another lot and combining them together and doing a study on those 12 pieces or would it be inaccurate because of two different lots?

Dawn,

Combining the two lots would create a bimodal distribution which introduces bias to your calculations. I believe that the answer is no. Don Winton (and I believe Howard Atkins?) dabble in the Advanced Statistics world and are probably a better source for a solution to your problem than me. I will offer my thoughts if no one can come up with anything.

Answers anyone?

Kevin,
Even if they were ran at the same time?

Dawn,

If they were run at the same time, material source was identical (i.e. same coil of steel used on the same machine with the same initial set-up) then you should be alright. Essentially all you have done was to split a single population into two similar lot populations. They should have the same properties. If you can be sure by the records that this is your case, then combining the two sample lots is probably fine (this is assuming that the distributions are normal and that they have similar standard deviations).

I was really hoping that one of the big guns would bail me out and give you something a little more solid for you. But I hope this helps you some what. Happy Holidays!!

Kevin,
It appears to me you are one of the big leagues.
Thanks for the help - I will use your information as a yes when I go back to work on Monday.
Merry Christmas and Happy New Year!

Dawn,

You should not have a problem using the two different lots as long as they are representative of the process.

The better answer, of course, is to select lots that are current and running and in a state of statistical control. "THERE IS NO CAPABILITY WITHOUT CONTROL." Ott and Schilling, Process Quality Control, 1990. I assume you already knew that.

Kevin’s point about the bi-modal effects is correct as far as ‘lots’ go and care should be taken. Your observations concerning the ‘lots’ would seen to indicate they came from the same ‘run’ in which case you should be OK and Kevin’s responses are accurate.

“Essentially all you have done was to split a single population into two similar lot populations.” Kevin, more correctly stated, “Essentially all you have done was to split a single population into two similar lot samples.” Just a small point. :>)

I apologize for not joining this thread sooner. The ice storm that blew through here wrecked havoc on power. I have just now been restored and do not know how much longer it will last.

Regards,
Don

Don,

Thanks for the bail out. It is appreciated from this end. Happy New Year by the way!

Regards,

Kevin

Don correctly pointed out that a capability study is valid when a process is in a state of statistical control (stabililty).

If Dawn were to use the 12 pieces and plot them on a an SPC chart, what chart should she use? An average and range chart could support n=2 and only 6 points to plot - not enough to show out of control conditions like 8 on one side, 8 trending and so on. An moving average and moving range may be suitable (described in Besterfield's Quality Control Book) to detect instability.

Also, could the 12 measurements be placed in a histogram and an examination for normality be suitable?

Just some more thought on the subject.

Kelly Speiser

Kelly (correctly) raises some valid aspects. As I pointed out above, capability studies are conducted after process performance has demonstrated statistical control for a minimum of 30 days (I prefer not to use the term 'stable' for various reasons I have expounded upon elsewhere in the forum). This does not have to be the case, but it is the norm. When exceptions to this rule are used, care should be taken.

Under the assumption that the process was monitored and determined to be in statistical control, process capability could then be taken directly from the process control charts. I assume this is not the case (incorrectly??), else a capability study would not be required at this point. This being the case, statistical control would need to be determined using the twelve samples in question.

The MA-MR chart Kelly mentioned is probably the better method to demonstrate statistical control, but normality? I am not sure. A twelve-piece sample (homogeneous?) is relatively small for a histogram, but it could probably be done. You may also use skewness and kurtosis from the raw data, which may (or may not) give a better indication of normality. Then again, there is always probability paper. : >)

Of course, all of my diatribe above may be a moot point. If Dawn conducts the study and the capability indicates a value of 1.33 or higher, further investigation may not be deemed required or necessary.

Regards,
Don

Kevin,

Good thoughts and not out on a limb at all. I have made several assumptions in my responses to this thread and you know what happens when you assume. Anyway:

What do you think?

Coming up. : >)

Is a two sample subgroup sensitive enough…

I believe you are thinking of an X-MR chart. The Moving Average (MA-MR) chart I mentioned is normally comprised of moving subgroups of three, which would give eleven data points to chart (I can expound upon this later if you like). This type of chart is not as sensitive as the typical Xbar-R charts, but are useable if you know the limitations. I suggested it as a mechanism that could (not should) be used to demonstrate control, if such a demonstration were required.

I’m thinking that you might be better off…

For this particular case, there are several methods, your suggestion being one, under the assumption (again) the data was available. From what I have assumed so far, I thought the process was not running and the twelve pieces were all that were available.

The one thing that keeps popping up…has been compromised

I agree. My head too. I (personally) have made it a practice to try to not perform capability studies unless I was sure (certain within a certain C.I.) of the integrity of the samples taken and the statistical control of the process. For a continuous process, the sample size should be based on tolerable error and confidence level desired, in addition to what I have pointed out earlier.

For example, standard deviation is estimated at 0.002, tolerable error is 0.001 and I want to be 95% confident in my results. NOTE: Standard deviation and tolerable error must be the same unit of measure, i.e. inches, meters, pounds, stones, kilos, electron volts, light years, warp factor, etc. Sample size is then n = [(1.96 * 0.002)/0.001]^2 or 15.37, rounded up to 16 (1.96 is from the Z table for 95% confidence).

The other tidbit of information needed would be is this a formal study (my customer is going to see and examine it) or an informal (I just would like to know). If the former, be prepared to demonstrate to the customer’s satisfaction the study is accurate and correctly performed. If the latter, the rules can be relaxed as much or as little as personal comfort level allows. I have relaxed (broken?) more of these rules than I care to recall. I am not a statistical purist, and hope I do not appear an ( o ) on the subject.

If I examine a study that purported to prove a process is capable, you can bet I am going to ask those types of questions. If I were the customer, your answers to those questions would determine if I accepted the study or not.

I have rambled enough. Does that answer your questions (concerns)? If not, lemme know.

Regards,
Don

Just a thought (going out on a limb),

Is a two sample subgroup sensative enough (sorta in agreement with Don on this point)? I'm thinking that you might be better off determining the capability of the larger split of the population and comparing the standard deviation of the 6 piece lot sample with the standard deviation of the larger population (chi square). Reject the null hypothesis and you may solve the issue. The one thing that keeps popping up in my head is as to the randomness of the sample and selected interval for the subgrouping has been compromised. What do you think?

Don,

Good stuff! Your assumption was correct regarding the Xbar-MR chart. I agree with your comment regarding the nature of the study and how it would be presented. Important considerations. Dawn put up a pretty good question, perhaps worthy of being on the CQE exam. Q&As just like this makes this forum quite a success!

WOW! All of this for 12 pieces? Boy, have I got my work cut out for me. Thanks for the info.

Kevin and Steven,

Glad you liked(?) it. Happy New Year.

Regards,
Don

Stephen:

Don't forget - It's not just what you do but that you understand why you're doing it and (every bit as important) being able to explain what you are doing and why.

Sound thoughts Marc. And yes, I liked it Don.

Happy New Year to the group! I hope 1999 is a good year for us all.

Good Post. I agree.

Regards,

Don

Subject: Inspection Criteria RE1
Date: Wed, 15 Sep 1999 09:20:54 -0400 (EDT)
From: Greg Gogates iso25@fasor.com
To: iso25@quality.org

Dear Group,

SNIP
> The most common use in the US seems to be if the uncertainty (k=something,
> usually 2) is less than some fraction of the tolerance, commonly 25% (10%
> traditionally, 25% in Z540, 33% in ISO 10012, ...) then the tolerance is used
> as stated. This corresponds to the ISO 14253 standard used with k=0. I admit
> that using the expanded uncertainty with k=0 doesn't make sense at first (at
> least it didn't to me when Ralph Veale explained to me how k=0 would be a good
> idea), but in the language of ISO 14253 it is actually a sensible description
> of current US practice.
SNIP

I believe that the 33% limit is obtained by assuming the upper and lower spec limit to be 3 sigma. If we relate this back to SPC practically:

Specification: 100 ± 1

the ± 1 is assumed a three sigma value and the 100 as the mean, now.........

ZONE A (Stable zone) would be the mean ± 1 sigma thus 100 ± 0.333

ZONE B (Warning zone) would be the mean ± 2 sigma thus ± 100 ± 0.667

ZONE C (Action zone) would be the mean ± 3 sigma thus 100 ± 1

This theory then also traces back to the Process capability indices
calculation which are given by Relative capability or Process capability

Cp = USL - USL / 6 sigma NOTE: to manufacture within specifications the distance between the USL (upper specification limit) and the LSL (lower specification limit) must be less than the width of the base of the normal distribution thus the distance between -3 sigma and + 3 sigma) If Cp is < 1, the process is not capable

Cp = 1, the process is marginally capable
Cp > 1, it indicates a potential for higher capability

and

Capability index
Cpk = the lesser of: USL - mean / 3 sigma or mean - LSL / 3 sigma
If Cpk < 1, the process is incapable
Cpk = 1, still some undetected non-conforming output
Cpk > 1 but < 2, still some non-conforming output but with a good chance of
detection
Cpk > 2, total confidence in the process.

I trust that this helps and makes some sense.

Regards in Quality
Frans J.C. Martins
South Africa