# The Metrics Conversion Challenge

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• #33691

Reigle Stewart
Participant

To all that are willing to accept the six sigma challenge:
Dr. Harry gave me the following problem some time ago and asked me if I could solve it (to help me better understand my six sigma metric skills and better appreciate the level playing field concept).  Now I pass it on to all of you.  It will really test your Six Sigma knowledge and provide some great insights along the way.  Believe me, this problem really pushed my understanding of performance merics to a new level.  If you can solve this one, there are several more that involve unit costs, cycle times and so on.  But lets tackle the simpliest first.
Problem Description: “All other things being equal, A certain corporate executive came to understand that one of his high volume factories (N=5,500 units per day) had several ways of making the same sub-assembly.  He asked for the capability data on each of the similar processes so he could select the best one.  Once selected, he would standardize on that process for subsequent transfer to other factories within the corporation.  After a couple of days, the following data and information was put on his desk.”
Question 1: Which process should be selected to standardize on?
Question 2: Which CTQ offers the highest quality?

Process A:
CTQ 1: DPU = .04, U = 34,678, M=25
CTQ 2: PPM = 4,378, U = 345, M=12,
CTQ 3: Y.ft = .97, U = 789,345, M=124
CTQ 4: Cp = 1.4, Cpk = 1.5, Ppk = 1.2, U=50, M = 5
CTQ 5: Y.rt = .68, U = 234,564, M = 256
CTQ 6: Pp = .95, U = 5,000, M = 34
CTQ 7: DPMO = 6,328, U = 243,649, M = 12
CTQ 8: D = 28, U = 1,832, M=345

Process B:
CTQ 1: Cp = 1.37, Pp = 1.1, M=25
CTQ 2: DPU = .09, U = 578, 456, M=12,
CTQ 3: Y.rt = .87, U = 879, M=124
CTQ 4: Cp = 1.2, DPMO=2,654, U = 25, M = 5
CTQ 5: Pp = 1.2, U = 34,567, M = 256
CTQ 6: PPM = 14,329, U = 2,367, M = 34
CTQ 7: D = 1, U = 1,438, M = 12
CTQ 8: Y.ft = .99, U = 189,832, M=345

Metrics Legend:
CTQ – critical to quality characteristics (key design feature)
DPU – defects per unit
DPMO – defects per million opportunities
Y.rt – rolled throughput yield
Y.ft – first time yield
D – number of observed defects
U – number of production units over which the metrics were computed
M – number of like CTQs per unit of product

Should you accept this challenge, I will be availible to answer questions (to a point).
Reigle Stewart

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#91622

Anonymous
Participant

can somebody do this problem.  this is problem like we have all the time we have problem like this.  we see so many different numbers in our factory but do not know how to make them go down to one or two we can all understand.  please some body that knows this method please do and post answer. i thank you so kindly.

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#91629

Mikel
Member

Reigle,
I’ll take your challange – I think it will take about 10 minutes once you provide me with good data. Right now there are some problems with your data. For example, for processA, CTQ 4, you have Cp = 1.4 and Cpk = 1.5. This is impossible.
So when you get your data straight, I’ll do it. Hint, I did not waste my time to see if you had other mistakes – it’s your data not mine. So check your work this time.

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#91632

Wanna See Stan Do It
Member

Stan, I saw this too.  But then I realized he said Dr. Harry created the problem as a learning exercise (or at least that is what was implied).  Based on this assumption I then began to seriously think about the problem statement, listed questions, and given facts.  At first, I too thought it was an error, but after studying it for a little while, I came to the following conclusion:
If Cp < Cpk and Ppk Ppk, then one of two things must be true.  Either the values are transposed or the Cp and Cpk measures were taken and at two different times.  Perhaps we are assuming they come from the same set of data.  If they were computed from different sets of data, they could naturally be different.  So I started thinking that maybe the Cpk value is not essential to the problem.  Maybe Dr. Harry through this in as a “wringer.”
If you think about it even further, the Cpk value is not germane to solving the problem, only the Cp and Ppk values because Cp is a “static” short-term metric and Ppk is a “dyamic” long-term metric (Cpk is a middle-ground metric and therefore not essential to understanding the extremes of capability).  Since M is the number of such CTQ’s per unit, then the short and long term DPU estimates for the given CTQ are not dependent upon the value of Cpk.
It would seem that what Mr. Stewart said about this problem stretching you mind is quite true.  Seems he hooked you.  Now that you have been proven to be wrong, we are awaiting your “do it in 10 minute” solution.

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#91637

Raja Setlur
Participant

Reigle,
Thank you very much for providing an excellent opportunity for neophytes and been-there-done-thats alike to sharpen their understanding. It is a welcome change from the mud-slinging that seems to be increasing on this forum.
I have two  doubts :
1.  Is it correct to infer that each M represents the opportunities for that particular CTQ and the sum of all M’s therefore the total no. of opportunities per unit ?
2. You have mentioned PPM twice but not given the legend for it. Does it indicate PPM out of  spec?
Thanks

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#91658

Statman
Member

Anonymous,

If you have problems like this in your factory, the ability to give Reigle the answer he is looking for is the least of your concerns.  You have two different processes producing the same sub-assembly and on one of them you measure the performance of one CTQ in RTY and on the other process you measure the same CTQ as Cpk?  Your data system is so bad that you report a Cp and Pp on the same process and same CTQ that are contradictory?  You actually give your Corporate Executive raw and inconsistent data?  If this is truly the case, it doesnt matter which sub-assembly process you choose because the factory is on the brink of chaos and about to spin into total chaos.

By the way, what Reigle is looking for as an answer is Gee I would have to convert all of these to a sigma value before I could compare them.  This is simply not true.  But let me give you some advise:

Measure the same CTQ on the two different processes with the same metric that is most appropriate to the situation.  If it is a variables CTQ use Cpk and PpK, if it is an attribute defect use PPM or DPMO.  If you are measuring throughput use RTY, etc.
Get your data systems straighten out so that there are standards for calculating metrics and eliminate the contradictions.
If you truly want to compare and choose the best process, dont be tricked into using a conversion to sigma level as the only way that this can be done.  You will be much better off using some method of decision analysis that preserves the original metric and allows weighting of importance across potentially competing attributes.  Try Kepner-Tregoe decision analysis, Pugh selection matrix, decision trees, or my personal favorite Desirability Analysis as it can model the diminishing returns of improvement.
Rarely will the choice of the best process be one of the original.  You will want to look for hybrids.  So you will need the preservation of the original metric.

By the way Anonymous, I will always post as Statman.  If I post under another Name I will let the users of this forum know that I have changed the name I use.  I find that people that post under different names in order to trick the users of this forum are using very poor etiquette and are childish.  Especially when they are resonding to their own posts.
Wouldnt you agree Anonymous?

Statman

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#91660

Cone
Participant

Hey there Statman.  You are the one that said its OK for people’s identity to not be known on this kind of website.  Now you are complaining.  I dont like people who hold double standards.

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#91663

Statman
Member

Gary,

I dont agree that I am presenting a double standard.  There is a big difference between posters keeping their identity unknown and posting under different identities only to create the appearance that others support their point of view.

Regards,

Statman

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#91664

Cone
Participant

Statman -:
How do you know wheter or not he is posting under different names?  You do not know this nor can you know this.  This is your suspicion.  This is not factual and you are making overtones that are quite unprofessional and unethical.  So you do hold double standards and you are obviously very biased.  You are begining to sound like that person called “Stan.”  Please Statman do not drop that low.

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#91665

Garth Brooks
Participant

No I am not the same Garth Brooks that sings.  I am the one that does statistical work.
If you have time between all of the arguing could you please work the problem that Reagle Stewman put out to iSixSigma.  I do not care about the trivia, just seeing a solution to the problem.  Several others have said this problem is “typical” for them and I must agree, so would somebody do the problem.

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#91668

Statman
Member

No Gary,
I do not know this nor can I know this.  I have never said that I know this.  I was stating that I will never engage in this practice.  Because I believe that anyone that does practice this is showing nothing but disrespect and contempt for the users of this forum.
If you want to infer to any individual that is up to you.
Statman

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#91669

Cone
Participant

Staman Sir;

“There is a big difference between posters keeping their identity unknown and posting under different identities only to create the appearance that others support their point of view.”  This is what you said plain and simple.  You certainly infered the violation in a big and pointed way.  Only a moron would not have made the connection.  This is maybe worse that what you accuse him of.  So do not try to escape what you said and what you infer.  Trying to make it ‘hypothetical’ does not absolve you of your own unprofessional transgressions and finger pointing.

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#91691

Mikel
Member

that person called “Gary”,
I object. Statman has much better manors than me and I can prove it with data. Don’t make such “factual” sounding claims without data.
that person call “Stan” (Stan for short)

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#91692

Mikel
Member

Proven to be wrong? I don’t think so. If someone presented me with such data, the first thing I would do is a sanity check – does the data make sense? It does not. When Reigle give reasonable data, I’ll do it in 5 minutes. I’ll take bets from anyone who thinks I can’t – this is trivial and stretches no ones mind. It is just data manipulation and made to seem hard by people who complicated instead of simplifying communication.
Give good data Reigle. Mr or Ms We Wanna See go find something worthwhile to do.

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#91694

Statman
Member

Oh.

I thought the You are beginning to sound like that person called “Stan” comment was a compliment.

Statman (That person called unprofessional and unethical)

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#91750

Mikel
Member

Reigle (or should I now call you Wanna See Stan? – I personally liked you better at BurtonCummings Jr or was than Randy Bachman),
Are you going to straighten out your data so I can work your trivial challange?

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