Reliability assessment for discrete time shock models via phase‐type distributions

Serkan Eryılmaz, Cihangir Kan

2020Applied Stochastic Models in Business and Industry28 citationsDOI

Abstract

In this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase‐type distributions. The well‐known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.

Topics & Concepts

Shock (circulatory)Negative binomial distributionMathematicsReliability (semiconductor)Statistical physicsApplied mathematicsGeometric distributionBinomial distributionProbability distributionStatisticsPhysicsPoisson distributionThermodynamicsMedicineInternal medicinePower (physics)Statistical Distribution Estimation and ApplicationsReliability and Maintenance OptimizationProbabilistic and Robust Engineering Design