There's no specific random element in the morale. The randomness comes from the situation. Many of the morale factors depend on certain thresholds for distances or proportions, and when a unit is near the threshold then which side it falls is essentially random unless you're doing the sort of laboratory condition experiments that Puzz does.
Also there is a lot of randomness in combat and shooting, which influences morale quite heavily.
Also there are no specific morale tests in Shogun, the morale of all units is evaluated every animation cycle.