Random Sum of Mixtures of Sum of Bivariate Exponential Distributions

Abstract

<b>Problem statement:</b> The distributions of R = X+Y and W = X/(X+Y), where X and Y follow Lawrance and Lewis`s bivariate exponential distribution, is generalized. <b>Approach:</b> In this research we found mixtures of sum of bivariate exponential random variables. <b>Results:</b> Also we calculated the probability density function (pdf) of the random sum of mixtures of sum of bivariate exponential random variables. <b>Conclusion/Recommendations:</b> In this study we investigated the pdf of random sum of mixtures of sum of bivariate exponential random variables

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

“…The reliability equivalence factors of the system is that factors ρ,0< ρ<1 by which the failure rates of some system components should be reduced to get a reliability for the system as that for a system obtained by assuming the improved methods mentioned above. We consider a system component with mixing lifetimes f 1 (t),f 2 (t),…,f m (t), the density function for this system can be write as follows, Everitt and Hand (1981), Akay (2007) and Teamah and El-Bar (2009) The original system: We derive the reliability and mean time to failure for the system with the mixing lifetime distribution. Assuming any mixed has the constant failure rate, λ i, i = 1, 2, …, m, Abu-Taleb et al ( 2007), Al-Kutubi and Ibrahim (2009), that is:…”

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

“…For example, a mechanical component, such as a load-carrying bearing or a cutting tool, may fail due to wear-out or when the applied stress exceeds the design strength of component material. Since the component or the tool can fail in either of the failure modes, it is then appropriate to describe the hazard rate by a mixed model, it is expressed as follows, Everitt and Hand (1981) and Teamah and El-Bar (2009):…”