Open AccessEvaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential Equations
Author(s) -
Khaled M. El-Said,
Mohamed S. El-Sherbeny
Publication year - 2005
Publication title -
journal of mathematics and statistics
Language(s) - English
Resource type - Journals
eISSN - 1558-6359
pISSN - 1549-3644
DOI - 10.3844/jmssp.2005.119.123
Subject(s) - mean time between failures , mathematics , reliability (semiconductor) , exponential distribution , failure rate , feature (linguistics) , differential equation , series (stratigraphy) , steady state (chemistry) , preventive maintenance , exponential function , differential (mechanical device) , reliability engineering , control theory (sociology) , statistics , computer science , mathematical analysis , engineering , power (physics) , quantum mechanics , physics , philosophy , chemistry , artificial intelligence , aerospace engineering , linguistics , biology , paleontology , control (management)
This study deals with the reliability and availability characteristics of two different series system configurations. The second system differs from the first system due to the additional feature of preventive maintenance. The failure times of a components are assumed to be exponentially distributed with parameters α,β,α' and β', respectively. The replacement time distribution of each server is also exponentially distributed with parameters γ, δ and θ. We derive the mean time-to-failure, MTTF, and the steady-state availability,AT(∞) for the two systems using linear first order differential equations and perform comparisons theoretically and graphically to observe the effect of the preventive maintenance on system performance