Journal of Mathematics and Statistics

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

Abdelfattah Mustafa and Adel A. El-Faheem

DOI : 10.3844/jmssp.2011.169.176

Journal of Mathematics and Statistics

Volume 7, Issue 3

Pages 169-176

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.

Copyright

© 2011 Abdelfattah Mustafa and Adel A. El-Faheem. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.