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You'll need a Liberty model with statistical variation tables and statistical static timing analysis. If you have the correct spice models you can extract the critical path and simulate with monte-carlo analysis for a few paths. Of course, this isn't practical for a large number of paths.
interface_timing=true is used for arbitrary cells that don't have a function or state table description. The timing arcs are used as-is with no attempt to validate them against a function. As such, this is not the best way to model a latch. If it's simple just use a "latch" group. If you...
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