The paper aims at clarifying the essential relationship between traditional probability density evolution equations and the generalized probability density evolution equation which is developed by the authors in recent years. Using the principle of preservation of probability as a uniform fundamental, the probability density evolution equations, including the Liouville equation, Fokker–Planck equation and the Dostupov–Pugachev equation, are derived from the physical point of view. It is pointed out that combining with Eulerian or Lagrangian description of the associated dynamical system will lead to different probability density evolution equations. Particularly, when both the principle and dynamical systems are viewed from Lagrangian description, we are led to the generalized probability density evolution equation.
Estimating reliability of degraded system based on the probability density evolution with multi-parameter
