Nonparametric Estimation of Performance and Performability for Semi-Markov Processes

Performability was introduced by Meyer (1980) [12] in order to generalize the notion of reliability and performance related measures. From a mathematical point of view this notion is defined by a sum or integral of a reward rate function defined on the state space of the system, known as an integral functional of the underling stochastic process. For a system described by a stochastic process ( ) 0 X t t , ≥ , with state space the set , and a reward rate function E g , we define the real-valued integral functional of X as follows