Metrika

, Volume 78, Issue 7, pp 807–827 | Cite as

A dynamic stress–strength model with stochastically decreasing strength

Article

Abstract

We consider a dynamic stress–strength model under external shocks. The strength of the system decreases with time and the failure occurs when the strength finally vanishes. Furthermore, there is another cause of the system failure induced by an external shock process. Each shock is characterized by the corresponding stress. If the magnitude of the stress exceeds the current strength, then the system also fails. We assume that the initial strength of the system and its decreasing drift pattern are random. We derive the survival function of the system and interpret the time-dependent dynamic changes of the random quantities which govern the reliability performance of the system.

Keywords

Stress–strength model External shock process Nonhomogeneous Poisson process Multivariate stochastic order 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of StatisticsEwha Womans UniversitySeoulRepublic of Korea
  2. 2.Department of Mathematical StatisticsUniversity of the Free StateBloemfonteinSouth Africa
  3. 3.ITMO UniversitySt. PetersburgRussia

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