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

Christos H. Skiadas () and Charilaos Skiadas ()
Additional contact information
Christos H. Skiadas: Technical University of Crete
Charilaos Skiadas: Hanover College

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 4, 1601-1611

Abstract: 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.

Keywords: Hitting time; First exit time; Inverse Gaussian; Extended Inverse Gaussian; First order approximation; Second order approximation; Fractional derivatives; Complicated systems; Human populations; Health state; Health state model; Death probability density; Car functional state; 26A33; 35R60; 60G22; 60G40; 60H15; 60H35; 62N05 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-019-09699-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-019-09699-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-019-09699-4

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().