Chapter List

1. Introduction

Industrial devices must be designed to prevent possible severe consequences from the failure of a device component. A way to ameliorate this design is to use probabilistic models of the device, from which technical and economical expectations can be drawn. Let us first give a mathematical background of such models. We consider a semi-Markov process ( ? _t) _{t ?0} taking its values in a finite space E. Let T ₀ = 0 and T _n ( n ? 1) be the successive jump times of this process. We assume that the semi-Markov kernel of the process has a density q with respect to the Lebesgue measure. This means that, for all i ₀, i ₁, , i _{n ?1}, i, j E, all 0 < s ₁ < < s _n,...