This is just an Excerpt from a larger document, click here to view the entire document.Introduction
For many years, Markov models and Markov analysis methods were relegated to that list of exotic but rarely used stochastic modeling techniques, at least for reliability and maintainability purposes. The promulgation of IEC standard 61508 Functional Safety of Electrical/Electronic/Programmable Electronic Safety-Related Systems has significantly re-vitalized Markov analysis by requiring the analysis of various disparate failure modes from a safety perspective. The methods also are receiving more attention because todays software tools make computationally complex Markov analyses easier to perform than in the past.
What is stochastic modeling ? A quantitative description of a natural phenomenon is called a mathematical model of that phenomenon. A deterministic model predicts a single outcome from a given set of circumstances; a stochastic model predicts a set of possible outcomes weighted by their likelihoods or probabilities. The word stochastic derives from Greek, to aim or to guess, and it means random or chance. Sure, deterministic, or certain are the antonyms. Such models are to be judged only on the models usefulness for the intended purpose.
The observer chooses to model a phenomenon as stochastic or deterministic. The choice depends on the observers purpose; the criterion for judging this choice is always the models usefulness for the intended purpose. To be useful, a stochastic model must reflect all those aspects of the phenomenon under study that are relevant to the question at hand. In addition, the model must allow the deduction of important predictions or implications about the phenomenon.
In reliability, maintainability, and safety (RMS) engineering stochastic modeling is used to describe a systems operation with respect to time. The component failure and repair times typically become the random variables.