How do I test for unequal variances in mixed model?

[#1]

I want to test if the measurement (intermediate) precision from two different labs are different. My data usually consist of the same sample being measured k times per day, across n days in each of the two labs. I analyze the data using Fit Model with lab as fixed effect, and Day as random effect. I would like to compare the total variation (within and between days) between the two labs - something similar to test for unequal variances in the Fit Y by X platform. Any ideas about how to do this in JMP?

As an example I use the '2 Factors Nested' sample data set. Treating Operators Sally and Willy as they were two different labs I wanted to compare, and treating Part as random, I get the following Fit Model output for each Operator: 

Sally measures with a total variation standard deviation of 0.43, and Willy measures with a total standard deviation of 0.58. I would like to test, if these are statistically different?

[#2]

I might be oversimplifying this, but would you get what you need by treating this as a measurement system analysis? Specifically, the Bias Comparison and Test-Retest Error options in the EMP personality tests if nuisance factors are measured differently. The picture below is from the 2 Factors Crossed data set, since you mentioned that each lab (Operator) is measuring the same part multiple times.

[#3]

just a quick add-on.  the MSA is a variance only model... a mixed model except without the fixed effect. 

[#4]

N_Sally = 12, N_Willy = 12, F(0.05, N_Sally-1, N_Willy-1) = F(0.05,11,11) = 0.355

U = SQRT(0.58)/SQRT(0.43) * SQRT(1/0.355) = 1.95 less than 2 (USP <1010>)， No significant different.

SQRT: Square Root

Refence: USP-NF 〈1010〉 Analytical Data—Interpretation and Treatment