Abstract
Problem statement: In reliability theory and operations research, there are many methods and techniques to improve the performance of a system. The aim of this study is to generalize reliability equivalence technique to apply it to a mixed failure lifetimes system f1 (t), f2 (t) with delayed time. Approach: We shall improve the system by using some reliability techniques: (i) reducing the failure for some lifetimes; (ii) add hot duplication components; (iii) add cold duplication components; (iv) add cold duplication components with imperfect switches. 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 some numerical results. 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.
Highlights
Operations Research, in its various fields, is concerned with the problem of system performance in the best possible way
There are two main such methods: Hot duplication method; in this case, it is assumed that some of the system components are duplicated in parallel
Cold duplication method: In this case, it is assumed that some of the system components are duplicated in parallel via a perfect switch
Summary
Operations Research, in its various fields, is concerned with the problem of system performance in the best possible way. Mustafa and El-Bassiouny (2009), introduced the to failure, say MTTF, as follows: reliability equivalence factor of the system such that the failure rates of the system’s components are functions of time t, studied two cases (i) the life time distribution
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