[R] lme4 2 factor factorial model with random factors

[Jacob Warren (RIT Student)]

Using lme4 how does one define a 2 factor factorial model with both factors
being random?

Specifically I am just trying to recreate the results from Montgomery's
Design of Experiments book (7th edition), example 13.2. In this example
there are 2 random factors and I want to include the interaction in the
model as Montgomery tests for significance in the full model first. I've
tried several things but cannot recreate the results in R. I would think
something like what's given below would work, but it does not.

lmer(y ~ (1 | Parts) + (1 | Operators) + (1 | Parts:Operators) )

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