Reliability equivalence factors for a series-parallel system of components with exponentiated Weibull lifetimes

Abstract

We study reliability equivalence factors of a system of independent and identical components with exponentiated Weibull lifetimes. The system has n subsystems connected in parallel and subsystem i has m_i components connected in series, i=1,...,n. We consider improving the reliability of the system by (a)a reduction method and (b) several duplication methods: (i) hot duplication; (ii) cold duplication with perfect switching; (iii) cold duplication with imperfect switching. We compute two types of reliability equivalence factors: survival equivalence factors and mean equivalence factors. Although our methods adapt to allow for general lifetime models, we use the exponentiated Weibull distribution because it is flexible and enables comparisons with other reliability equivalence studies. The example we present demonstrates the potential for applying these methods to address specific questions that arise when attempting to improve the reliability of simple systems or simple configurations of possibly complex subsystems in many diverse applications.