# Capability calculation of surface profile

#### Tahirawan77

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Hi,

I want to calculate the capability of my process. The variable is part thickness of the surface profile. The material thickness is measured at 5 different points within the part. See picture below for details

I have measured 30 parts and each part has 5 points as given in the picture. The target thickness and the tolerances of all the points is same which is 1mm±0.1.

In order to calculate process capability should I calculate a separate Cpk value for each of the points (P1…P5) so in the end I have 5 Cpk values or should I calculate Cpk for each part so I have 30 Cpk values (one for each part). Which is the correct approach?

#### Jim Wynne

The variable is part thickness of the surface profile.
Are you measuring just thickness, or surface profile?

#### Tahirawan77

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Are you measuring just thickness, or surface profile?
Hi Jim,

I am only measuring the thickness and it should be uniform across the surface profile.

#### Jim Wynne

I am only measuring the thickness and it should be uniform across the part. the surface profile.
Using the phrase "surface profile" confuses things. A few more questions: What's the purpose of the capability study? How are you measuring the thickness? How can you do a capability study with just thirty parts?

#### Tahirawan77

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Using the phrase "surface profile" confuses things. A few more questions: What's the purpose of the capability study? How are you measuring the thickness? How can you do a capability study with just thirty parts?

Basically the purpose of the study is demonstrate to customer that we meet the minimum requirement specified by the customer 1.33 and to be sure in future the parts produce will meet the thickness requirement.
The part in question is measured with a contact less laser scanner.
We have a low volume production of composite parts and we do a 100% check of all parts and then annual volume is less than 100 parts.

#### John C. Abnet

Super Moderator
n order to calculate process capability should I calculate a separate Cpk value for each of the points (P1…P5) so in the end I have 5 Cpk values or should I calculate Cpk for each part so I have 30 Cpk values (one for each part). Which is the correct approach?

Good day @Tahirawan77 ;
Do 5 or 30 different processes manufacture the thickness? Remember, this is a "process capability" study. I would expect all data to be collected into ONE (single) capability study. Please help me understand why there would be more than one Cpk result for this thickness feature ?

Thank you.

#### Tahirawan77

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Good day @Tahirawan77 ;
Do 5 or 30 different processes manufacture the thickness? Remember, this is a "process capability" study. I would expect all data to be collected into ONE (single) capability study. Please help me understand why there would be more than one Cpk result for this thickness feature ?

Thank you.
Thanks for your reply and good day to you as well @John Abnet
We do have other molds which produces the same part so in order to increase the sample size can I combine parts produce in different mold (but similar design) into one study?

Regarding more than one cpk. pls see below picture to get an idea what i mean

#### Jim Wynne

There is no way to derive a meaningful Cpk result from a 30-piece sample. The first basic rule of Cpk analysis is that the samples must come from a process that has demonstrated statistical control. Also, such "studies" are missing a very important element: chronology. You need to understand how the process acts as time passes. The fact that production is limited to only ~100 pieces per annum simply means that no Cpk study should be undertaken. This should be explained to the customer.

#### John C. Abnet

Super Moderator
Thanks for your reply and good day to you as well @John Abnet
We do have other molds which produces the same part so in order to increase the sample size can I combine parts produce in different mold (but similar design) into one study?

Regarding more than one cpk. pls see below picture to get an idea what i mean

View attachment 28598
Good day @Tahirawan77 ;
Including multiple molds will result in bi-modal results.
What I am suggesting is that each mold represents its own set of process data. (i.e. each mold = a process). ALL data (from each of the "5 points [i.e. regardless of how many points the data is collected],, = a single "process". Therefore all of the data collected for all samples of a single mold= a single process capability study. This would then need repeated for each mold.

(don't forget to take into account sample size considerations as mentioned by @Jim Wynne )

Hope this helps.
Be well.

#### Semoi

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First of all I would strictly differentiate between the point estimate of the Cpk value and the associate uncertainty. There is nothing inherently wrong with using only a few measurements to calculate a Cpk value, however, the uncertainty of this estimate is probably large. In addition, you should make sure that all parties (you and your costumer) use the same formula to calculate the Cpk estimate. Different methods exists, because the Cpk value uses the standard deviation of the population, and you have to agree on an unbiased estimator -- the formula, which is used for the Cpk value.

Using multiple measurements per part ensures that your data analysis becomes complicates: Assuming that the measurements "within" a single part are correlated, you either have to use advanced data analysis, or you have to find a way to get rid of four data points. The reason for this is that the data points are not independent -- in the statistical literature you have performed "pseudo sampling" also called "sub sampling".

Although I understand that you want to make sure that the part has an homogenous thickness and no point lies outside the tolerance range, you should decide how to condense these five points into a single number, which incorporates the information of interest. E.g. if all five measurements are practically the same number, you could keep only the first data point -- it basically contains all the information. Instead, if you generated inhomogenous parts you probability should use the maximal value of the absolute deviation, max{ | zMeasured - zTarget| } for each part. Note, that due to the absolute value the tolerance is now single sided.

Personally, I get the impression that you and your customer did not properly specify the expected outcome of the study. Thus, I expect that your customer is not firm in statistics. In my experience it is not helpful to discuss statistics with such a counter part, because they are neither able to decide what is needed nor able to select a practical method to achieve this goal. Hence, I suggest that you first perform the calculation describes above -- it will take only 20min -- and then talk to the customer. If you communicate the short comings and uncertainty of the data analysis you have a high chance that the customer is already satisfied. Especially if you send the data and offer that the customer could perform some data analysis themselves.