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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/424ABCD7-CDA0-4151-9D26-10E2C443818F | ||
| Year | 2020 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | C. H. Skiadas and C. Skiadas, “The first exit time stochastic theory applied to estimate the life-time of a complicated system”, Methodol. Comput. Appl. Probab., vol. 22, no. 4, pp. 1601–1611, Dec. 2020. doi: 10.1007/s11009-019-09699-4 https://doi.org/10.1007/s11009-019-09699-4 | ||
| Appears in Collections |
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.
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