# Capability Rollup

Six Sigma – iSixSigma Forums Old Forums General Capability Rollup

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• #47666

Savage
Participant

I was talking with a co-worker the other day and he mentioned that in a previous company they used a method of capability rollup. BAsically calculating the capability of subassemblies and them combining them to result in a rolled up, composite capability metric. Kind of like RTY, but using CpK instead. My friend didn’t have much detail about the method. Has anyone done this? Is this a valid method? Any resources for me to research? Just curious – thanks.Matt

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#159148

M. Salim MSA
Participant

I have done that using Z scores to rollup scores from parts, process, product, software etc into one score for the company ! This is done using scorecards for Z-values and rolled up into one final score ….

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#159149

Participant

Why would you want to? Whats the value behind it?

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#159151

Savage
Participant

That’s what I’m wondering.  I can’t imagine a reason for doing this.  I am trying to understand if there is some statistical justification for doing this.

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#159152

Participant

Matt, there is known. Its stupid

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#159153

M. Salim MSA
Participant

Stupid for some ….. overall six sigma level for others !

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#159154

M. Salim MSA
Participant

Key is to have the understanding of a capability score rollup !

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#159164

Participant

OK, then explain to me how 3 sigma * 3 sigma = 4.1 sigma?????????
Then Explain Why this useful. I have a complete and open mind.

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#159223

Savage
Participant

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#159225

M. Salim MSA
Participant

I can send you some examples if that will help ….. I was referring to the other gentleman when I mentioned “understanding” ! some people are curious which is good …. but some people don’t have the understanding nor do they have the ability to understand !

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#159226

Jim Ace
Participant

Matt:

This is how I learned to do this task.  From my example you will see why you can not just average the Cpk values or Z scores

Step 1: Find the yield of X independent items.
Example: 5 indpendent items were found to have the following yields;
X1=90%, X2=95%, X3=99%, X4=84% and X5=73%.  The 5 items could be the number of steps in a process or the parts in a subassembly.

Step 2: Multiply the 5 independent yields.
Example: .90 x .95 x .99 x .84 x .73 = 0.51904314.  This is the rolled throughput yield

Step 3: Find the average yield
Example: 0.519043^(1/5) = 0.877082995.  Notice that 0.51904314 = (0.877082995)^5, thus confirming that the average yield is NOT the mean of the item yields.

Step 4: Convert average yield to a Z score
Example: Excel equation =normsinv(0.877083) = 1.160527733

Step 5: Add 1.5 sigma to estimate the average short term capability
Example: 1.16 + 1.50 = 2.66.  This is your overall Sigma score for the 5 independent items.  Notice that the overall Sigma of 2.66 is NOT the mean of the subordinate sigma scores.

Summary:

Item                  Yield            Sigma (Z)
X1                      0.900                2.78
X2                      0.950                3.14
X3                      0.990                3.83
X4                      0.840                2.49
X5                      0.730                2.11
Overall              0.877                2.66

Jim Ace

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#159264

Savage
Participant

Thanks Jim.  Just before I read your post, I found the same method in one of my reference books.  Thanks again.

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