ABSTRACT
A system submitted to shock and wear failures is studied. The shocks cause deterioration and the system is preventively repaired after a number fixed of them. There are internal failures that cause the failure of the system, these failures are correctively repaired. Shocks arrive following a Markovian arrival process. The failure and repair times are modeled by phase-type distributions. Under these assumptions the system is studied. The multidimensional Markov process governing the system is constructed. The availability and the rate of occurrence of the different types of failures are calculated. A numerical application illustrates the calculations throughout the system. The procedure we follow for studying the system is known as matrix-analytic methods, these allow us to obtain algebraic expressions for the main results that are calculated and consequently to implement them computationally.
