# Process capability

Six Sigma – iSixSigma Forums Old Forums General Process capability

Viewing 37 posts - 1 through 37 (of 37 total)
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• #36675

Sowmya
Member

How to find Cp and Cpk
Sowmya

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#106424

Pawan Anand
Participant

Sowmya,
What r u collecting data on?
Regards,

Pawan

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#106426

Member

Calculate as follows:
Cp: usl-lsl/6 sigma
cpk: usl-Xbar/6 sigma; Xbar-lsl/6 sigma.
The denominator 6 can be a value of  3,4 sigma depending upon the study being carried out.

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#106431

RubberDude
Member

The Cpk formula you gave is not the one I am use to seeing.  Maybe you know something I don’t, but I’ve used this same formula for 25 years:
Zu = (USL – Xbar) / sigma  (usually S for sample std dev)
Zl = (Xbar – LSL) / sigma
Zmin = Minimum value of Zu or Zl
Cpk = Zmin / 3
For a six sigma capable process, Cpk must equal a minimum of 2.0
I’m open for any discussion about this.  Like I say, there may be some new idea about the value of Cpk, but I’ve always used the above.

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#106436

Brian.P.M.
Participant

Most of the formulas that I have seen use sigma hat (R bar/d2) for the calculations, derrived from the average range of the samples.
Cp= (USL-LSL)/6 sigma hat
Cpk= min of (USL-X dblbar)/3 sigma hat OR (X dblbar-LSL)/3 sigma hat
If you are using the calculated sigma of the individuals then you have Pp & Ppk.

BrianPM

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#106445

RubberDude
Member

Thanks, Brian, for the reminder.  I think I must have had my “sigma-dunce-hat” on this morning.  “Sigma-hat” completely slipped out of my thought pattern.  I usually refresh my (nowadays 2 sigma) memory by pulling a reference book (like the gool ol’ reliable Juran “blue book”) and looking up the formula for verification.
At any rate, you are right.  Cpk calculations should use “sigma hat” or “estimated standard deviation.”

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#106447

Brian.P.M.
Participant

No problem. We all have days like those.
BTW I don’t  recall seeing your name around here but, then again I’ve only been following this forum for about 8-9 mos. New here? If so welcome, this is a great resource.
Regards,
BrianPM

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#106449

RubberDude
Member

Brian,
Yes, I’m new here.  I’ve only been “snooping around” the forum for a week now.  I’ve got 25 years of related experience, with the “knowledge” but not the certification of SSBB.  I’m due to start the BB cert journey Q1 of next year and hope this will get me “more readier” for it.  And, yes, I’ve already found it to be a great resource, so long as you “weed out the chaff” and ignore some of the “swelled heads”…. Typical of internet resources, I guess.
But good to have guys like you that take the forum seriously as a help those struggling.
Thanks for the welcome!

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#106457

Stevo
Member

Brian, welcome to the forum, heres a little info that I gleamed so far.  The posters will fall into several categories:

Expert
Wannabe expert
Stalker
Blow hard
Smart-ass
Wallflower

And there are several clubs:

JO Club
Pro Harry
Against Harry
Stan (several people make up that one)

I for one, lean towards the Smart-ass category, but some day hope to become a stalker.

Stevo

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#106461

BH
Participant

We need to add one more category… Lurker.
Welcome to the forum.
bh

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#106477

Mikel
Member

You forgot to mention that the smallest, most exclusive club is the pro Harry club, which has somewhere around 3 less members than the Stans.

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#106482

Member

Mr. RubberDude
Your formula is absolutely right. Thats an alternative. The ASQC recommends the formula which I have sent.cpk value should be 1.5 not 2.0 for a six sigma quality. More info. can be derived from Mario perez wilsons book, Leavenworth and Grant.
Thanx

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#106494

RubberDude
Member

Can you please tell me where ASQ (ASQC had a name change about 8 years ago) references their preference for a particular formula for Cpk?
Also, since Cpk is derived by dividing the distance from process average (Xbar) to the specification limit (USL or LSL) measured in standard deviations (typically sigma-hat), to attain six-sigma status(Zmin = 6), Cpk would have to be 2.0 (6 / 3 = 2).  A 1.5 Cpk would indicate a Zmin value of 4.5 (4.5 / 3 = 1.5).
Ideal would be to have Cp = Cpk = 2.0
Am I wrong on this guys?

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#106495

Brian.P.M.
Participant

Hey Rubberdude,
I think he may be invoking the infamous 1.5 sigma shift…But that is a whole different debate
As for a 6 sigma process I think you need a Cp of 2.0 with a Cpk of 1.5, I think.
Check this…
http://www.sytsma.com/tqmtools/proccapanal.html
BrianPM

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#106496

DaveS
Participant

Brian PM
Nice link except he states that with shift,worst case is 6.8 ppm.
This is not correct.
If you buy the 1.5 shift idea ( don’t use it myself as it is no value add), it still would be impossible for a process to shift to 4.5 sigma from the center on both sides at once. Worst case would be 4.5 on the one side (3.4 ppm) and 7.5 ( less than 1 part per trillion,I think) on the other. At least the shift-ites got the 3.4 right!

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#106497

walden
Participant

Brain.P.M.,
The Sigma Value is based on short term variation (Cpk), so a 6 Sigma process would have a Cpk of 2.0. With a 1.5 sigma shift the long term Sigma Value (Cp) would be 4.5 (Cp of 1.5).
The reference you cited states that Cp would be 2.0 if the process were centered. When the process is centered Cpk = Cp.
Thanks,
Chris

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#106498

RubberDude
Member

Brian,
Thanks for the info and link.  And, yes, the 1.5 shift rule is a Motorola standard, understanding that this is for sample purposes and must be followed by long-term data supporting that the mean truly DOES shift within the center 3 sigma band of the tolerance.  In my posting, I stated that the IDEAL would be Cp = Cpk = 2.0.
I don’t subscribe to the 1.5 sigma shift theory, as I think it is statistically unsound in its assumptions.  The theory that process mean will shift is true, but seems like few “gurus” follow that up with the fact that process variation (sigma) will ALSO shift and could have an effect on the overall distribution curve.  AND, less we forget, we ARE dealing with the assumption that the process distribution curve is “normal.”
In Badri’s initial posting, he stated:
“cpk: usl-Xbar/6 sigma; Xbar-lsl/6 sigma.
The denominator 6 can be a value of  3,4 sigma depending upon the study being carried out.”
I have never seen any reference to using a different denominator to calculate Cpk.  If there is a reference to being able to chang the denominator, I would like to review it.  The only change is the required results for Cpk.  Changing the denominator would be like changing the conversion factor for centimeters to meters or inches to feet.
So, if your customer has a requirement of minimum Cpk = 1.5, and you have a Zmin of 3, then change your denominator to 2 and everyone will be happy….. right?
“Tortured data will confess anything” (author unknown)

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#106501

Mikel
Member

That would be wrong. A six Sigma process would be a Cp of 2 , Cpk of 1.5. Go read any of the Motorola or Mikel Harry stuff.
In todays’s capability .it is a Cp of 2, and a Ppk of 1.5.

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#106502

Mikel
Member

The ASQ materials are just a rip off of Mikel Harry’s materials that were a rip off of what was done by the original implementors at AlliedSignal – mainly Steve Zinkgraf.

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#106503

Brian.P.M.
Participant

For the record, I don’t subscribe to the 1.5 shift either. I was just pointing out where the poster’s 1.5 Cpk may have come from. Under that assumption, in order to have a 6 sigma process you would only need a 1.5 Cpk. A 6 sigma process, by Moterola’s definition, has 3.4defects/million (Zmin4.5). A true 6 sigma process (Cp=Cpk=2.0) would operate at a parts/billion level (assuming a normal distribution).
I feel that a well controlled/charted process should be able to avoid the rule of thumb shift and I would rather look at historical data and see what the actual drift of the particular process really is.
As for variable denominators, I’ve never heard of that one either.
BrianPM

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#106504

Thai
Participant

That’s good to know.  I have always wondered where much of the original instruction material came from.  I especially wondered after comparing my circa 1998 SBTI material against another person’s SSA material.  Much of the material was identical slide for slide.
That comment explains a lot.
Thanks
Kirk

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#106505

walden
Participant

Oops, I really lost it there. Of course, Cpk can never be greater than Cp.
Thanks for the correction. It’s been a long week. Thankfully, it’s almost over.

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#106506

RubberDude
Member

Brian,
Well said!!

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#106507

New
Participant

Stan,
Are you saying that SSA training materials came from Steve Zinkgraf and SBTI (or Allied Signal)?

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#106508

Brian.P.M.
Participant

Thank you

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#106509

Anonymous
Guest

Brian,
I also welcome your post, but I feel that as far as this forum is concerned that matter is still unresolved.
The status is as follows: a few weeks ago a poster questioned the whether the Beta risk of consecutive subgroups was sufficiently high to warrent using a 1.5 sigma guardband, or bias.
Gabriel responded by pointing out that the Beta risk for the first subgroup was 50%. He also proposed a method using much larger subgroups to reduce the Beta risk.
There are also other charts that are more sensitive to shifts, such as the Cusum chart.
As yet, no-one has demonstrated that a process can be ‘qualified’ after an adjustment, such as a furnace tube change, using a single subgroup on an X-bar and R chart.
While I agree with you that a ‘constant shift’ is not required, and is contrary to the spirit of corrective action implicit in SPC, as yet Mr. Reigle has not accepted any of the counter arguments for the dubious shift.
Regards,
Andy

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#106515

Mikel
Member

I am saying that the structure and content that everyone has copied originated with the original AllidSignal material. Most of that content came from Steve.

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#106531

Allied Signal Manager
Participant

I was a training manager within Allied Signal at the time of
their Six Sigma deployment. The original material came
from the prime contractor for the deployment which was
the Six Sigma Academy in Scottsdale Arizona. Steve
Zinkgraph was an employee of the Six Sigma Academy at
the time when Six Sigma was first introduced. Steve was
an instructor and used the Academy materials when the
deployment was first launched. Later on during the
deployment Steve Zinkgraph was hired away from the
Academy by Allied Signal and then developed his
materials based on the original Six Sigma Academy
content. This was true for several other SSA instructors
as well. Prior to this Steve Zinkgraph had no materials
from which to train Black Belts so the Academy materials
were used across the company until each business unit
could develop their own versions of the SSA content. I
am very familiar with this history because of my many
corporate meetings on this subject and the many
discussions with Rich Schroeder who was the VP of
Operational Excellence for Allied. Later on in the
deployment Rich Schroeder left Allied and joined the Six
Sigma Academy as their CEO and Steve Zinkgraph
stayed on at Allied. This pattern of content evolution was
also used by General Electric. I know this because I
worked with several of the GE training managers to make
it happen.

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#106536

mjones
Participant

Interesting bit of history.
At first I was ready to strongly disagree with Stan’s post: The ASQ materials are just a rip off of Mikel Harry’s materials that were a rip off of what was done by the original implementors at AlliedSignal – mainly Steve Zinkgraf.
Further posts put it further into perspective. And here’s some more history for you:
When ASQ began offering open enrollment BB classes it was not a “rip off” of SSA materials. There was a partnering contract between ASQ and SS Academy, and ASQ had access and permission to use SSA materials for training. However, the SSA materials did not work well with the diverse ASQ classes, e.g., SSA had little on discrete data or transactional processes. So the ASQ instructors substantially modified some SSA content but much of it was actually replaced with material developed from scratch to fit ASQ training needs.
A few years later when the ASQ-SSA relationship was dissolved, all the SSA content had to be removed. This was not hard to do because, by then, very little of it “belonged” to SSA.
So where did the ASQ content come from? From the instructors who developed it.
And the instructors came from? Major companies who had implemented SS.
And who were these companies? There were several, but there was strong representation from, of course, Allied-Signal. So you form your own opinion of the evolution of materials among SSA/Allied Signal based on other posts.
But, to be clear about ASQ: the ASQ folks did not ‘copy’ or ‘steal’ or ‘rip off’ any training materials. Slides and content that had been used somewhere else or even appeared to be ‘owned’ by anyone were not used. ASQ was very concerned about actual violation, and even the appearance of the violation of any copyright/trademark infringements. But, certainly the general knowledge, philosophy, types of examples (perhaps different numbers and context, but making the same point), etc., reflected a combination of the best info around at the time. No doubt, the Allied-Signal content influenced the ASQ content, especially in the early days. I suppose that someone looking at that material could get the impression they were copied. They simply were not.
I’d bet that today, with the turnover of instructors, updating and changing of content, ASQ has virtually nothing that looks or feels like Allied-Signal stuff any more.

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#106538

Allied Signal Manager
Participant

It is very likely that mjones is right about the ASQ-SSA
relationship. I have little knowledge about that
partnership. I do believe that ASQ is a reputable
organization and would not “rip off” any other persons
material. That just don’t happen very often with
professional societies. Consultants are another story.
As with anything that is new and of value it will undergo
continuous evolution and refinement. My post was limited
to the Allied Signal days when SSA was the prime
contractor for assisting the deployment of six sigma
across the company. I really laugh when I hear other
consultants claim they deployed six sigma within Allied
Signal knowing they were just an instructor at the time.
The original SSA materials were also modified by several
of the European business units of Allied Signal. This
evolution had nothing to do with Steve Zinkgraph. The
Allied Engine group did not use Zinkgraphs evolution
either. They used another SSA consultant’s material as a
base. At the root of all the evolutions of content were the
“core” SSA books. It was these books that got the ball
rolling. It is difficult to pick up another persons slides and
go teach them, so a rewrite is virtually inevitable over
time. Seems that every consultant says the other
consultant’s material is poor and their’s is better. I believe
they say this because of the not invented here syndrome.
How many ways are there to show a slide that teaches
the mean and standard deviation?

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#106555

Helper
Participant

Cp = Eng or design tolerances/6 Sigma
Cpk Upper Spec Limit:  When the central tendency is closer to the upper spec limit = Upper Spec Limit – Xbar/3sigma.
Cpk Lower Spec Limit:  When the central tendency is closer to the lower spec limit = Xbar – Lower Spec Limit/3sigma.

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#106562

Brian.P.M.
Participant

And so are you…
It is Cp=(USL-LSL)/6 sigma hat
Cpk=Min(USL-Xdbl bar OR Xdbl bar-LSL)/3 sigma hat
BrianPM

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#106575

Mikel
Member

MJones.
Whenever you are ready, I will more than happy to sit with you and compare AlliedSignal’s matrials, ASQ’s SSA materials, and their current materials. The examples have evolved to suit the diversity of the students, but little else. I have copies of each including many of the consultants materials that claim to be “superior” today. The basic content has not changed.

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#106576

Mikel
Member

ReigleS,
I have been wondering where you were. You may want to use full disclosure here and tell everyone that you were not really an AlliedSignal Manager (a real AlliedSignal manager would know how to spell it)
Your version is totally incorrect. The SSA cartoon books were indeed sold as intellectual property to AlliedSignal and GE, but not used because they were unusable. Steve did indeed develop what was used at everywhere except the AlliedSignal Aerospace business. They used materials developed by Bill Ross which also had nothing to do with the SSA cartoon series. Bill used JMP instead of Minitab as well.
The original GE “MBB” training used the cartoon book and it was actually taught by Mikel. This “training” has been the subject of jokes within GE ever since.
Show of hands from former Allied and GE employees – how many of you used the cartoon books and of those of you that used them, how many of you actually learned Six Sigma from them?
I’ll take bets on the results (you may be wanting to come up with another group of screen names to go with the 50 or so you already use)

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#106586

RubberDude
Member

If “mjones” is who I think he is, he would know very intimately about the ASQ-SSA relationship and history.  If you compare ANY statistical training material, it will always look very similar.  I mean, jeez….. How many ways can you describe the normal distribution curve?
Right Mike?
RubberDude <— (an mjones protege')

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#107732

Sowmya
Member

What is central tendency

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#107783

Orlando
Participant

Hi Allied Signal Manager
Some people on this Forum know me because everytime someone starts talking about the beginnings of Six Sigma I interupt and try to give them a clear picture of what the beginnings looked like.  Well anyway I won’t go through the whole debate I had on this forum but I want to post an interesting FAX sent to Mario Perez-Wilsons organization dated August 7, 1990.  My wife keeps telling me to clean the garage and throw out those Motorola papaers but I keep telling her than I want to write a historical account of Six Sigma.
The FAX was sent from Stephen A. Zinkgraf.
August 7, 1990