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

Abstract

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 f 1 (t),f 2 (t),…,f m (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.

Reliability Assessment of Bridge Structure Using Bilal Distribution

“…Additionally, Mustafa [10] examined the reliability equivalence factor, investigating a series configuration in which component failure rates adhered to both Weibull and linearly increasing distributions. Mustafa and El Faheem [11,12] expanded the scope of the reliability equivalence method by integrating both mean and survival reliability equivalence metrics. Papaioannou and Straub [13] utilized the concept of a sensitivity analysis based on reliability gradients.…”

Improving the performance of the series parallel system with linear exponential distribution

“…Mustafa [2], applied the reliability equivalence factor techniques to a system consists of n independent and non-identical components connected in series with mixed constant failure rates. Mustafa and El-Faheem, [4], generalized reliability equivalence factor technique and applied it to a system consists of m independent and non-identical lifetimes distributions with mixed failure and delayed lifetimes rates. Xia and Zhang [12] applied the reliability equivalence factor of a parallel system with n independent and identical components distributed as Gamma life time distribution.…”

“…It is assumed in this method that the component is duplicated by another standby one with a perfect switch. 4. Cold duplication with imperfect switch method.…”

Reliability Equivalence Factors of a System with 2 Non-identical Mixed Lifetimes and Delayed Time

“…, applied the reliability equivalence techniques to a system consists of n independent and non-identical components connected in series system, which have mixing constant failure rates. Mustafa and El-Faheem (2011), generalized reliability equivalence technique to apply it to a system consists of m independent and non-identical lifetimes distributions, with mixed failure lifetimes f 1 (t), f 2 (t),…,f m (t). In this article, we consider a system with mixing lifetimes, delayed time.…”