Reliability Equivalence Factors of a System with m Non-Identical Mixed of Lifetimes

Problem statement: The aim of this study is to generalize reliability equivalence technique to apply it to a system consists of m independent and non-identical lifetimes distributions, with mixed failure lifetimes fi(t),f2(t),...,fm(t). Approach: We shall improve the system by using some reliability techniques: (i) reducing the failure for some lifetimes; (ii) add hot duplication component; (iii) add cold duplication component; (iv) add cold duplication component with imperfect switch. We start by establishing two different types of reliability equivalence factors, the Survival Reliability Equivalence (SRE) and Mean Reliability Equivalence (MRE) factors. Also, we introduced a numerical illustrative example. Results: The system reliability function and mean time to failure will be used as reference of the system performances. For this reason, we obtain the reliability functions and mean time to failures of the original and improved systems using each improving methods. Conclusion: The results can be used to distinguish between the original and improved systems performances and calculate the equivalent between different cases of improving methods.