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The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System

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  • Christos H. Skiadas

    (Technical University of Crete)

  • Charilaos Skiadas

    (Hanover College)

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.

Suggested Citation

  • Christos H. Skiadas & Charilaos Skiadas, 2020. "The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1601-1611, December.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-019-09699-4
    DOI: 10.1007/s11009-019-09699-4
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    References listed on IDEAS

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    1. J. Janssen & C. H. Skiadas, 1995. "Dynamic modelling of life table data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 35-49, March.
    2. Christos H. Skiadas & Charilaos Skiadas, 2015. "Exploring the State of a Stochastic System via Stochastic Simulations: An Interesting Inversion Problem and the Health State Function," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 973-982, December.
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