Reliability equivalence factors of a general parallel system with mixture of lifetimes

The aim of this work is to discuss reliability equivalence technique to apply it to a general parallel system consists of n components, with independent and nonidentical mixture of lifetimes and delayed time. We derive the reliability and mean time to failure of the original and improved systems according to reduction, hot duplication, cold and imperfect switch duplication methods, respectively. Reliability equivalence factors are introduced to compare different systems. The α-fractiles of the original and improved systems are calculated. Two types of reliability equivalence factors of the system are obtained. Numerical results are provided to interpret how one can utilize the theoretical results obtained in this work and to compare the different reliability factors of the systems, some special cases are introduced.