Hello, I am Yusuke Ono, Senior Tester at JMP Japan.
It seems that your model is a variance component model (or a random effect model). You can fit a (one-way) variance component model on JMP by the following steps.
(1) You need to prepare two variables in the input data.
The one is the continuous response variable which contain measurments. The other is the nominal group variable, which is "Run" in the example. Note that you need to set the "Run" column to Nominal.

(2) Select [Analyze] > [Fit Model]. The Fit Model window is launched.
(3) Set the response variable (or the measurment variable) to [Y].
(4) Select "Run" variable, and click [Add] button in the Construct Model Effects panel.
Select the "Run" variable in the Construct Model Effects, and click the red triangle icon for the [Attributes] and select [Random Effect].

(5) Click [Run] button.
(6) Go to the REML Variance Component Estimates table. Rihgt-click somewhere in the table,and select [Columns] > [Sqrt Variance Component]. This shows standard deviations of variance components.

Note that these variance estimates are estimated by REML (restricted maximum likelihood, residual maximum likelihood). If your data is not balanced, these results are different from EMS(Expected Means Squares, or moment method). The difference between REML and EMS is summarized in the following document page.
https://www.jmp.com/support/help/en/18.2/index.shtml#page/jmp/mixed-models-and-random-effect-models....
If you want to do MSA (measurment system analysis), JMP has a specific platform for MSA.
The Measrument System Analysis platform can be invoked by [Analyze] > [Quality and Process] > [Measrument System Analysis].
Yusuke Ono (Senior Tester at JMP Japan)