# Cpk to percent and to Yield calculation

Discussion in 'Lean, Six Sigma and DFSS' started by essegn, Sep 3, 2018.

1. ### essegnMember

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Dear Sirs,

i would like to define a future process, but i am stucked with Cpk values and Yield. I am not able to calculate them, in order they fit together.

Moreover, i am not able to recalculate Cpk to Yield. I found several conversion tables, but the results differ.

In the process, following needs to be checked:

Parameter 1: Cpk should be 1 - continuous
Parameter 2: Cpk should be 1 - continuous
Parameter 3: Cpk should be 0,85 - continuous
Parameter 4: Cpk should be 0,85 - continuous
Parameter 5: 95% - variable

How do i calculate an Yield?
In my case would be the Yield also the Rolled Throughput Yield.

Many thanks.

2. ### essegnMember

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Here is what i calculated:

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Cpk = Sigma (Z) / 3

Cpk=1 = 3 Sigma = 66807,2 ppm = error rate 6,68% or Yield 93,32%
Cpk=0.85 = ca. 2,5 Sigma = Yield 85.25%

The whole YIELD:
Parameter1 x Parameter2 x Parameter3 x Parameter4 x Parameter5
0.9332 * 0.9332 * 0.8525 * 0.8525 * 0.95 = 60%

It seems to too creepy.

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In the Minitab i found that to the sigma level 3 correspond Cpk=1 and the failure rate 96.75% and to Cpk=0.85 the failure rate 93.06%.

Then: 0.9675 * 0.9675 * 0.9306 * 0.9306 * 0.95 = 77%

This seems to me okay.

What do you think?

3. ### judeguActive Member

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@essegn Sorry, man. I don`t think your calculation is exactly correct. Just using Cpk, you can`t get YIELD. You need the USL,LSL and the data which is used to calculate Cpk.
And the prerequisite is that you assume your process is a normal distribution.
PS: The easier way is just using the Minitab. When the software calculates the Cpk value, it also calculates the defect rate.

4. ### MinerModeratorStaff Member

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The differences that you see in the various tables may be due to the assumptions made. Some tables have been created with the assumption that the process mean does not move over time. Other tables have been created with an assumption that the process mean will drift over time, decreasing the yield and increasing the failure rate. The amount of this drift may vary from table to table, but an expected drift of +/- 1.5 sigma is commonly used.

5. ### essegnMember

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Thank you for your replies.
I have found out already, that the relationship in Minitab between a Cpk and a defect rate differs.

In any of quality guidelines for suppliers are listed Cpk and / or Ppk values - requirements for a minimal capability of the process.
This is why i wanted to how, how these requirements could be translated into yield.

But back to the origin question:
I have no data. It is a new product that is currently in the development phase. My task is to define requirements under which the process could be taken over from the development to the production.
How to set the Cpk values, which could be later recalculated into Yield?

I mean something like:
Feature 1: Cpk must be more than 1
Feature 2: Cpk must be more than 1
Feature 3: Cpk must be more than 1,33

Yield needs to be more than 85%.

How could be the required Cpk values recalculated into Yield? If with such Cpk values is possible to achieve for example Yield of 85 percent.

6. ### essegnMember

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I have made a few simulations in Minitab and i need to admit, that judegu has right. There is no realtionship between Cpk and Yield. Even when the data are normaly distributed, it depends on how they are distributed ("outliners") - Yield is changing while the Cpk value is constant.

But the question is still the same: How could be a future process defined? Every parameter / every feature of the product with a Yield / a defect rate or NCC ?

7. ### judeguActive Member

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There are some very good articles talking about Cpk and Ppk in the Resources Section. You can learn a lot. Hope it will help you.
And how to calculate or predict the future Yield with Cpk? As I mentioned before, you need the actual Sample data, USL and LSL.
First, use minitab/Excel to find your process`s average and standard variance. (A big "IF" here is your process is a normal distribution.)
Second, calculate the defect rate at the your process left tail and right tail.
right tail defect rate = 1- norm.dist(USL, average, standard variance, 1)
left tail defect rate = norm.dist(LSL, average, standard variance, 1)
NOTE: I am using the function from Excel.

Then, get the yield. Yield = 1- (left tail defect rate + right tail defect rate)

NOTE: I don`t take into consideration the process drift here.

Last edited: Sep 5, 2018
8. ### ncwalkerWell-Known Member

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Cpk has the process limits baked in. It is possible to calculate yield from Cpk. But you need Cp as well. Cpk is going to be against the closest limit, so you're yield number will only the the percentage out of the window on that side. Not the other. For that you need Cp as well to determine what the total tolerance is.

9. ### Bev DModeratorStaff Member

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Oh for Pete's sake. The calculation of mathematical formulas is no substitute for thinking. Nor are theoretical models any good at predicting actual yields. The whole Cp/Cpk thing went totally off the rails when we conflated the capability index with defect rate. I understand the power of seduction of the mathematical approach but our parts are built on real manufacturing lines by real human beings and not by a theoretical distributional model*. Compounding this is the fact that most processes are simply not homogenous and the sampling used for the Cpk calculation is too small and too constrained to give us a real picture of total variation of the process.

all this work for a theoretical answer that doesn't match reality.

I get that some Customers ask for this calculation (which frequently drives the under sampling and further manipulations to get an acceptable answer). The answer is rarely correct so we shouldn't put so much time into how to 'tweak' the calculation to make it different.
If you are in development make some parts under varying conditions and factors that vary in the same way they will in production and do the
graph it against the spec limits, check for stability and calculate the actual yield. .
If you are in production phase get some time series data from the actual process and graph it against the spec limits, check for stability and calculate the actual yield.

if you don't understand rational subgrouping, non-homogeneity and it's effect on SPC and other calculations - spend your time researching this, not how to convert Cpk into yield.

*paraphrased from Donald Wheeler.

10. ### ncwalkerWell-Known Member

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Your clouding the issue with logic. ;-)

There's good statistics. Then there's also getting your customer off your back so you can get work done.

11. ### essegnMember

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Many thanks for your replies. I really appreciate that.
Ncwalker: I tried today some Minitab simulations again, but the results were rather confusing. Now it seems to me that the Cp value is the key. Thank you.
Bev D: There is necessary to have in any development goals or boundaries. Such words, to do something and see what happens seem off-date to me. We are able to do one product in a day, therefore we need to have process / Yield / Cpk - whatever specifications to do not spend much time when samples are ready and and somebody needs to judge them.