Shock and Wear Models under Matrix-analytic Methods

Abstract: A device subject to shocks arriving randomly is considered. Every shock can be fatal or not. The shocks follow a Markovian arrival process. When the shock is fatal, the device is instantaneously replaced. The Markov process governing the shocks is constructed, and the stationary probability vector calculated. The probability of the number of replacements during a time is determined. Particular cases of interest are studied and a numerical application is performed. The expressions are given in algorithmic form. Computational aspects are introduced. This model extends other previously considered in the literature.