Flaws in science/engineering/software due to pseudo random generation?

I am trying to see if there were any incidents in the past where using PRNG or not accurate randomness scheme leaded to wrong conclusion in research.

For example, a lot of fields today use simulations to predict natural science results and I was wondering what are the best practices and if there were any flaws due to bad randomness in the past.

For security purposes it's clear that one has to use encrypt lib random function, but for science or simulation of physical systems I am not sure it's the case. My guts say it should be the same, but I am not sure how to justify it.