Mathematics to handle variance accurately and calculate probability correctly

Abstract

While I was working for an automobile company, I realized that in various designs and model analyses, by expanding the values, handled in the calculations from points to a distribution with a range and using that distribution as the calculation object, it became possible to handle the variation precisely, and a high level of performance and reliability could be achieved in various developments. After that, I have released tools that can realize complex design calculations and simulations as distributions. It is clear that calculations based on probability distributions can significantly improve calculation accuracy compared to the standard deviation and Monte Carlo method that have been commonly used.