# Z=6, Cpk=1.5 or Ppk=1.5

Six Sigma – iSixSigma Forums Old Forums General Z=6, Cpk=1.5 or Ppk=1.5

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• #40228

KS
Participant

I need help to undestand the relationship between Cpk/Ppk & Zscore values. As a standard practice, the capability of any process in six sigma, we represent with Z score of short term & ppm of long term.
Hence,Z=6, PPM=3.4, Here in reverse if we look, PPM=3.4 corresponds to Z=4.5 with Zshift=1.5. Also, we know, Z=3xCpk. Hence, Z=6, means Cpk=2 & Ppk=1.5. Is it correct?
Here which one is more appropriate to represent Z score & Capability index relationship –
a) Z=6, DPMO=3.4, Cpk=2 or
b) Z=6, DPMO=3.4, Ppk=1.5 or
c) Z=6, DPMO=3.4, Cpk=1.5(with 1.5 sigma shift).
I appreciate help in this regard.
thanks
ks

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#124240

“Ken”
Participant

ks,
Why do you need so many ways to characterize the capability of your processes?  Perhaps you or your company would do well to settle on the use of either Capability, Performance, or Sigma(Z) value to use instead of all, or combinations.
Cp and Cpk use the short-term standard deviation to compute process capability.  Pp and Ppk use the long-term standard deivation to compute process performance.  There are some on the forum who advocate using Cp for potential, and Ppk for actual.  Yada, yada, yada…  When the process is stable and predictable the difference between either sets of process indices is within 15%.  This difference is well within the confidence intervals for either capability/performance estimates.  So, I personally would settle on one of the two, and keep life simple.
Sigma or Z-value to me is a composite capability estimate useful for management updates and/or presentations.  If calculated properly, it is useful for comparing to other Z-values from other processes.  So, from a strategic perspective you should keep it for management reporting.
There is no right or wrong answer to the question of more “appropriate”.  Rather, the answer is based on your needs, and the needs of your organization.
Ken

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#124250

KS
Participant

Ken,
I agree that Z value is a composite measure but people are more familiar with Cpk/Ppk, to explain them a relationship between Z=6 & capability/performance indices, I wanted to understand which one will be more appropriate to compare. From clarity point of view can you help me undesratnd Z=6 is equvivalent to Cpk=1.5 or Ppk=1.5.
I feel it shall be Ppk=1.5 but in some material it is mentioned as Z=6, equivalent to Cpk=1.5. Can you clarify.
regards
ks

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#124252

Peppe
Participant

Try to draw  what represent Z and what cpk/ppk and find the relations. The answer will come up easly.  Do not consider “1,5 shift” can add confusion.
Rgs, Peppe

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#124253

KS
Participant

for me Cpk represents short term capability & Ppk, long term capability. Cpk represents within variation & Ppk total variation.
Actually, I am trying to develop a slide ruler where I want to show relationship for people to understand it easily.
On a slide rule if Z=6, DPMO=3.4, Cpk=?, Ppk=?. This is my question.

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#124254

FF
Participant

The following statements are equivalent if you assume Zshift=1.5:
Zst=6, Zlt = 4.5, Cpk=2, Ppk = 1.5, DPMOlt = 3.4

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#124260

hari
Participant

Z=6, Cpk=2.0 if you have only one sided specification limits. Otherwise, you can’t compare or calculate Cpkbased on Z value as Cpk is the minimum of Cpu and Cpl.
But if the process is centered at the Target(middlepoint of USL and LSl) then Cp=2.0, Z=6

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#124261

Geckho
Participant

The more I read these posts and realize how confused the majority of people are when it comes to calculating Z-scores, taking shifts into account, etc., I begin to question the validity and usefulness of Z-scores at all (collective *gasp* from the Six Sigma world).
It seems to me that so many people use these measures improperly or don’t understand what the measures are telling them that I wonder how many Sigma scores out there are utterly meaningless, both as an internal measure and as a tool for comparing processes.  Not to mention my general disdain for the infamous “1.5 shift” that I have been posting about.  There are so many more accurate and simple measures out there that give much more information, I seldom even look at the Sigma score anymore.  It’s almost become more of a convention that everyone calculates just because “it should just be there”.  Or worse yet, an uninformative bragging tool more than anything else.
Well, my process is at 5 Sigma…beat that!
(Most people who make a claim like this, in my experience, fail to mention that their capability analysis only reflected a yield of 230 DPMO, but they slapped that handy Z-shift in there for good measure :). )

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#124275

“Ken”
Participant

ks,
From a comparison perspective, I work with a Sigma value of 2 being equivalent to both-Cp=2 and Cpk=1.5.
Ken

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#124283

“Ken”
Participant

Geck,
Accuracy in capability measures is really not the issue, precision is the true issue.  What all of us are attempting to do is estimate the expected defect rate using a Normal distribution approximation of our data in the tail regions.  For discrete data it usually takes thousands of values to come even close to this approximation.  For continuous data it usually takes hundreds of values.  So, remember all we are really trying do is establish a basis for making good business decisions in the face of variation using a common measure.
Good luck in your pursuits for the truth.
Ken

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#124288

Geckho
Participant

Ok, one thing that I know for sure is that if I want to measure something to make good decisions about it, one of the first steps is to validate my ability to measure it, right?
Why don’t you and I create a pile of capability data with the random number generator in Minitab.  Then, we distribute the collection of data to a randomly selected group of Black Belts (heck, we could even select them from the same large corporation, if you like) and ask them to calculate the Sigma values from it.
My only point is that I would be willing to bet that this little MSA would score quite poorly.  Therefore, should this measuring system really be something that we use to make sound business decisions?
I’m not calling the measure itself into question.  Not by any stretch.  What I am calling into question is our ability to truly call it a “universal measure” when it seems like everyone you talk to has their own “little rules” about how to calculate it.  Even when practitioners have the same rules, they often have them for different reasons.  How is a new Black or Green Belt (not to mention manager) supposed to make any sense of it?  The answer is the best that they can, which usually results in even more creative interpretations added to the pile of confusion.
(Incidently, I’m one of those freaky people who value the discussion even more than the conclusion, in many cases.  In my mind, “devil’s advocacy” is a science ;)  )

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#124303

“Ken”
Participant

Geck,
I’ll pass on the MSA experiment.  I agree with your general comments, and I’ll add another.  The Sigma measure supports each opportunity in a unit of work, not the entire product or service system.  It’s 3.4 defects per million for each opportunity, not 3.4 defects per million.  This a major point of confusion for about 85% of the folks doing Six Sigma.
What’s the difference?  Imagine you tell your customers that your quality level is 5-Sigma on the way to 6.  That’s ~200 defects per million for each opportunity, and you have 100 value-add steps to produce the product.  What is the expected defect level of the completed product at a 5-Sigma level of quality?  You guessed it,  ~200 dpmo X 100 V-A opportunities = 20,000 dpm’s, or a 2% defect rate.  Not great quality in final product today.  This is the real reason why some businesses need to drive to higher quality levels, complexity.  It is also the reason why customers of some companies doing Six Sigma never really see the value.  In fact, what a company with 100 value-add steps needs to do is look at ways to reduce process complexity, eliminate the non-value add, trim the value-add complexity by redesign, and and then look at way to improve quality to higher than 5-Sigma.
Try to remember what this Six Sigma approach is really about–customer-focused, results-driven, and process-oriented.  It’s about building a learning organization, and capturing the learning for others to see and understand.
Yes, there are some wrinkles in the measures.  But, if these measures are consistent across the company you’ve achieved a great thing.  Everywhere in the company you’re speaking the same language, and hopefully, hopefully measuring the right things.  In the final analysis, if the math is a little off, it’s really not that big of a problem.  Today, a market leader needs to be able to change with the customer in a manner of weeks not months or years.  Today, a market leader need to make business decisions on facts, not gut feel.  Today, a market leader prepares their employees for the battle by insuring they have the tools, methods, and support necessary to meet the competition head on.  All that said, the measures are important, but only a part in the game of achieving market leadership…
I have enjoyed our discussions, but now have to move on to more pressing engagements.
Regards,
Ken

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