A dynamic stress–strength model with stochastically decreasing strength
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.
KeywordsStress–strength model External shock process Nonhomogeneous Poisson process Multivariate stochastic order
- Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt Rinehart and Winston, New YorkGoogle Scholar
- Finkelstein M (2008) Failure rate modelling for reliability and risk. Springer, LondonGoogle Scholar
- Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New YorkGoogle Scholar
- Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New YorkGoogle Scholar