CPK - 2 Dimesions

[#1]

Dears,

a "conceptual" question...

If I have a characteristic identified by two factors and the specification limits are defined by an area rather than an interval... is it possible to calculate the CPK?

See the diagram below (invented): blue dots = the specification, orange dots = production.

Is it possible to calculate a CPK?

Thanks in advance for the feedback.

[#2]

Hey @SimonItaly ,

I have also pondered this question!  I have not found anything readily available but have worked on a possible solution on my own, though it is just a fun side project and nothing formal.  What I did was fit a distribution for the Y axis values and then fit a distribution to the x axis values.  I then simulated a million values using random distributions of the best fit for Y and X.  I then calculated the out of spec percentage from the simulation and aligned that with an out of spec/Ppk curve and reported the Ppk for the out of spec percentage observed.  The main downside to this method is if your out of spec calculation returns zero you get an error.  However, you might just have to up the simulated values from a million to get at least one out of spec value.

Not a formal approach but something that I found worked for my situations.  Hope it at least spurs some ideas!

Steve

[#3]

Hello Steve,

thanks for the feedback, your experiences and suggestion.

This could be useful for an initial evaluation ("draft").

I could good to have some feature (also in JMP) to have a full simulation on this topic (now I spoke on 2 dimesions... but it could be needed also for more the 2 dimensions).

Thanks again... and we hope that JMP developers will thinks on this needs.

Have you a good start week.

Best regards,

Simone

[#4]

If you wish to have feature for this, please create a wish list item to JMP Wish List

[#5]

Hey @SimonItaly ,

Here is an example of the output I get from a script I wrote that follows the methodology mentioned above(I used the Semiconductor Sample data set and the A1 column that I made a summary table from extracting the Min and Max's of each Wafer):

this dashboard shows the Simulated data (Sim) vs the real data (R)

If predicted Out of spec = 0% then predicted Ppk = 2

Just food for thought!

Steve

[#6]

Hello Steve,

thanks for sharing.

Very interesting and source of good information.

In my past experiences... I worked more that 20years in the Semiconductor Sector and your case study is very clear.

Best regards,

Simone

[#7]

Since your question is "conceptual" in nature, I will ask why would you want to calculate the Cpk?  How do you intend on using this?  Sorry, I will admit my bias is such metrics are not very useful.  This due to the following reasons:

1. The enumerative statistics used in the calculation are estimates and how well they describe the true population is often in question (e.g., used a 30 piece sample without any explanation as to how the sample was obtained).  When Cpk's are reported, they are reported as one number even though there is obviously a confidence interval around both of the statistics used in the metric.

2. When the Cpk does not meet your objective, you are left with disaggregating the metric to determine if it is a mean or variation problem.  Why not just "track" those (mean, deviation from target and standard deviation, minimize)?

3. There is often misuse of Cpk's for comparison (e.g., comparing across different products)

4. How often is stability established before Cpk's are reported?

5. Specifications are often inappropriate.

see: 

Gunter, Berton (1989) “The Use and Abuse of Cpk”, Quality Progress, January 1989

Can you please supply a real example of the situation you describe, where there is a specification (customer requirement) on the "area"?  

If I understand the situation you describe, could you first understand the relationship between the 2 factors and the response variable (area), then, perhaps using tolerance parallelograms (see Shainin), understand the appropriate specs for each factor and use traditional Cpk for each factor independently?

[#8]

Dear Staman,

thanks for the feedback and good input/suggestion.

In my specific case, the object is characterizied from 2 variables (indipendent).

The values of this 2 characteristics (in the same time) can be only inside the elliptical area I draw before.

In took/measure, some real parts and I plotted this part in the graph.

The target is to evaluate/estimate (similar to CPK approach) how many parts I can have out of specification (out of elliptical area).

I imaged a concept similar to CPK... but in 2 dimension.

I do not know if my thoughts.

Thanks again.

Best Regards,

Simone

[#9]

My personal feeling is not CPK. But rather a comprehensive evaluation of two indicators.
Suggest considering two dimensional weights and then evaluating after dimensionality reduction. Or use the simplest weighted average analysis.

[#10]

Dear Frank,

thanks for the feedback (appreciated).

My situation is that the 2 variables are indipendent... and I would like to evaluate/estimate in "some way" how many parts could be out of the "eliptic specification area" with some data collected from real production line.

I hope to be clear in my explanation.

Thanks again... and have you a good start week.

Best Regards,

Simone