Research Article Open Access

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

Abdelfattah Mustafa1 and Adel A. El-Faheem2
  • 1 Department of Mathematics, College of Science and Humanitarian Studies, Al-Kharj, University, P.O. 83, Al-Kharj 11942, Saudi Arabia
  • 2 Department of Mathematics, Faculty of Science, South Valley University, Aswan, Egypt


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 f1(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.

American Journal of Applied Sciences
Volume 8 No. 3, 2011, 297-302


Submitted On: 31 December 2010 Published On: 25 March 2011

How to Cite: Mustafa, A. & El-Faheem, A. A. (2011). Reliability Equivalence Factors of a System with m Non-Identical Mixed of Lifetimes. American Journal of Applied Sciences, 8(3), 297-302.

  • 13 Citations



  • Mixture distributions
  • reliability equivalence
  • improving system
  • exponential distribution
  • numerical illustrative
  • equivalence factors
  • theoretical results
  • reliability functions
  • duplication method
  • Mean Reliability Equivalence (MRE)