How do I get confidence intervals for % of Total in Variance Components for Gauge R&R?

[#1]

Good afternoon!

I have a question: is it possible to calculate confidence intervals for % of Total in Variance Components for Gauge R&R?
Is there documentation or formulas where I can see how the calculations are performed?

Thanks in advance!

[#2]

Right-click on the header of the table 

[#3]

I tried it, but it only gave confidence intervals for the Variance Components, but not for % of Total.

[#4]

Quality and Process Methods > Variability Gauge Charts > Variability Gauge Analysis Report Options >... is most likely good starting point for the documentation

[#5]

Thanks a lot!

[#6]

Hi @SignalFerret615 : What you seek is very complicated. It involves finding a confidence interval for a ratio of variances (each being a linear combinbation of variances!); and intervals on even the simplest of ratios can be challenging indeed. The ratio can be linearized perhaps and then numerical methods can be used to find the confidence interval, but even then there are a load of moving parts.  

Linearization, for example,  can be carried out via: ratio = (VC[repeat]+VC[repro])/(VC[repeat]+VC[reprod]+VC[part-to-part])

Some algebra results in L = VC[repeat] + VC[repro] -ratio*(VC[repeat] + VC[repro] + VC[part-to-part])=0. Then get the upper bound of the confidence interval for L for some value of ratio. Then used fixed-point interation (https://en.wikipedia.org/wiki/Fixed-point_iteration) to find the value of ratio that makes the interval =0. You could do a similar thing to get the lower bound.

You'll need to use methods like the following:

https://www.sciencedirect.com/science/article/abs/pii/016771529190118B

https://www.tandfonline.com/doi/abs/10.1080/00949659008811240

[#7]

Hi!
I have to try this!
Thank you so much!

[#8]

Hey @SignalFerret615 ,

this is along my wishlist item here:

Add 95% confidence intervals to MSA outputs - JMP User Community

Maybe kuddo's it and add in your wish as well