51. The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System.
- Author
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Skiadas, Christos H. and Skiadas, Charilaos
- Subjects
PROBABILITY density function ,STOCHASTIC systems ,TIME perception ,STOCHASTIC processes ,FOKKER-Planck equation ,POPULATION - Abstract
We develop a first exit time methodology to model the life time process of a complicated system. We assume that the functionality level of a complicated system follows a stochastic process during time and the end of the functionality of the system comes when the functionality function reaches a zero level. After solving several technical details including the Fokker-Planck equation for the appropriate boundary conditions we estimate the transition probability density function and then the first exit time probability density of the functionality of the system reaching a barrier during time. The formula we arrive is essential for complicated system forms. A simpler case has the form called as Inverse Gaussian and was first proposed independently by Schrödinger and Smoluchowsky in the same journal issue (1915) to express the probability density of a simple first exit time process hitting a linear barrier. Applications to the health state of biological systems (the human population and the Mediterranean flies) and to the functionality life time of cars are done. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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