We present two stochastic failure models for the reliability evaluation of manufacturing equipment that degrades due to its complex operating environment. The first model examines the case when the environment is a temporally nonhomogeneous continuous-time Markov chain, and the second assumes the environment is a temporally homogeneous semi-Markov process on a finite space. Derived are transfor...

We develop a methodology for characterizing the superposi-tion process of N 2 discrete-time arbitrary on/oo sources. The superposition is a discrete-time semi-Markov process with O(2 2N) states. We use the superposition model to analyze a nite-buuer statistical multiplexer with multiple arbitrary on/oo input sources. We study the eeect of various traac parameters on the queueing performance.

This paper introduces the hhsmm R package, which involves functions for initializing, fitting, and predication of hidden hybrid Markov/semi-Markov models. These models are flexible with both Markovian semi-Markovian states, applied to situations where model absorbing or macro-states. The left-to-right series/parallel networks states two states. also includes switching regression as well auto-re...

Probability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to metaphorical gateways and transitions between past future [...]

We study two versions of multistable Lévy motion. Such processes are extensions of classical Lévy motion where the stability index is allowed to vary in time, a useful property for modelling non-increment stationary phenomena. We show that the two multistable Lévy motions have distinct properties: in particular, one is a pure-jump Markov process, while the other one satis es neither of these pr...

Model-checking is a method of verifying concurrent systems in which a state-graph model of the system behavior is compared with a temporal logic formula. This paper extends model-checking to stochastic real-time systems, whose behavior depends on probabilistic choice and quantitative time. The speciication language is TCTL, a branching-time temporal logic for expressing real-time properties. We...

The notion of N-ple Markov process is defined in a quite general framework and it is shown that N-ple Markov processes-arel inear combinationso f some martingales

Production and non-productive equipment and personnel delays are a critical element of any production system. The frequency and length of delays impact heavily on the production and economic efficiency of these systems. Machining processes in wood industry are particularly vulnerable to productive and non-productive delays. Whereas, traditional manufacturing industries usually operate on homoge...