Hamed Lorvand

‎Large engineering infrastructures such as power grids‎, ‎communication systems‎, ‎and cyber-physical systems are exposed to shocks of varying intensity and scope‎, ‎which due to the dependence between components‎, ‎can cause successive failures throughout the entire network‎. ‎The classical reliability models are generally based on the assumption of independence between components ...

In reliability theory, various [ ]-shock models are used to study the shock-exposed systems that are sensitive to the length of intershock times. In this paper, a new generalized [ ]-shock model is introduced and studied, under which a system fails when the intershock time is smaller than a threshold [ ] or larger than another threshold [ ] for the first time, where [ ]. Reliability characteristics of the corresponding lifetimes are investigated under the new model when the intershock times follow an arbitrary distribution. As an illustrative example to demonstrate the practical aspects of the new model in the real world, we discuss the reliability behavior of an adult heart. Furthermore, we present an application of the discrete-time version of the new model in agricultural engineering. Numerical examples illustrate our theoretical findings.

In this paper, we consider a k -out-of- n system subjected to shocks arriving through a Bernoulli process, that is, the shocks can change from their initial values to only two possible values. Assume that each input shock to the system can lead to the failure of some components. Two scenarios are examined here, in the first scenario it is assumed that at least one component fails with probability one, and in the second scenario we assume that at least one component fails with probability θ . Then, the reliability and an optimal replacement strategy for a k -out-of- n system under these scenarios are investigated. With the proposed scenarios, a closed form for the likelihood function for systems in Markovian and non-Markovian regimes are then derived. A model for the preventive replacement policy of the system is also presented. Numerical examples are also given to illustrate the theoretical results.

Consider a k -out-of- n system consisting of L types of components, L=1,2,…,n such that the number of components of the l th type is n _l , l=1,2,…,L . Let this system is exposed to external shocks, and each entered shock may fail some components of the system. The system fails when at least n-k+1 components fail. In this paper, we study the reliability of this system under a shock model. In addition to reliability analysis, we investigate a preventive maintenance policy for this system to reduce abrupt failures. Numerical examples are also provided to illustrate theoretical achievements.

Consider a k-out-of- n system which is subject to shocks that arrive at random times. This study develops [ ]-shock model, among the variants of well-known shock models, for such system which consists of independent components. In a [ ]-shock model, the system fails when the inter-arrival between two consecutive shocks is less than a critical threshold value of [ ]. Depending on the number of components that fail due to the occurrence of the shocks, we introduce two [ ]-shock models. The reliability function and mean time to failure of the system are discussed when the time between shocks has an arbitrary distribution. Furthermore, the problem of finding the optimal preventive time concerned with minimizing a mean cost per unit time is investigated. Numerical examples based on a simulation study are also provided to illustrate theoretical achievement.