Evaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential Equations

Abstract

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 &#945;,&#946;,&#945;' and &#946;', respectively. The replacement time distribution of each server is also exponentially distributed with parameters &#947;, &#948; and &#952;. We derive the mean time-to-failure, <em>MTTF</em>, and the steady-state availability,<em>A_T(&#8734;)</em> 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

Stochastic Modeling of Repairable Redundant System Comprising One Big Unit and Three Small Dissimilar Units

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New sufficient condition of Discrete-time systems of neural networks

“…In recent decades, neural networks have been extensively studied in many aspects and successfully applied to many fields such as pattern identifying, voice recognizing, system controlling, signal processing systems, static image treatment and solving nonlinear algebraic system (Alfaris et al, 2008;Bay and Phat, 2002;Bezzarga and Bucur, 2005;El-Said and EL-Sherbeny, 2005;Lekhmissi, 2006;Sen, 2004;2005a;2005b;Sen et al, 2005;Sharif and Saad, 2005;Waziri et al, 2005). Such applications are based on the existence of equilibrium points and qualitative properties of systems.…”

The Delay-Dependent for Discrete-Time Systems

“…Recently, the problem of delay-dependent stability analysis for time-delay systems has received considerable attention and lots of significant results have been reported; see, for example, Chen et al (2003), Bellomo and Bellouquid, 2006;Brezzi et al, 2007;El-Said and EL-Sherbeny, 2005;Lekhmissi, 2006) and the references therein. Among these references, we note that the delay-dependent stability problem for discrete-time systems with interval-like time-varying delays (i.e., the delay d (k) satisfies 0<d m ≤d(k) ≤d M ) has been studied in (Alfaris et al, 2008;Bezzarga and Bucur, 2005;Brezzi et al, 2006), where some LMI-based stability criteria have been presented by constructing appropriate Lyapunov functionals and introducing free-weighting matrices.…”