Technical note Unavailability analysis of safety systems under aging by supplementary variables with imperfect repair E.A. Oliveira, A.C.M. Alvim * , P.F. Frutuoso e Melo COPPE/UFRJ – Nuclear, Caixa Postal 68509, 21945-970, Rio de Janeiro, RJ, Brasil Received 24 May 2004; accepted 15 June 2004 Available online 8 October 2004 Abstract A method was developed for the reliability analysis of systems of components whose failure rates may be time-dependent. A special case of such systems is the one whose components are under aging. The hypothesis of minimum repair is adequate in many cases, especially in heavy industries, such as the nuclear industry. The method employs the technique of supplementary variables to cast the modeled Nonmarkovian systems into Markovian ones. Use is made of the Laplace transform technique, in order to reduce the number of equations, which are then solved by numerical methods. The inverse Laplace transforms to obtain the final solution of the set of differential equations is also done by using the Gauss–Legendre quadrature meth- od which is very fast. Applications to safety systems, like the auxiliary feedwater system of a typical PWR plant show that the method is very fast and accurate as compared to other sim- ulation methods. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Unavailability analysis; Aging; Supplementary variables; Imperfect repair; Bad as old repair; Laplace transforms; Gauss–Legendre quadrature 0306-4549/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2004.06.003 * Corresponding author. Tel.: +55-21-2562-8441; fax: +55-21-2562-8444. E-mail addresses: eugenio@lmp.ufrj.br (E.A. Oliveira), alvim@con.ufrj.br (A.C.M. Alvim), frutuoso@ufrj.br (P.F. Frutuoso e Melo). Annals of Nuclear Energy 32 (2005) 241–252 www.elsevier.com/locate/anucene annals of NUCLEAR ENERGY