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