Development and application of a model for stochastic systems Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/s1784q983

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  • Occasions arise in engineering for conducting probabilistic analyses concerned with the "state" character of systems which range in scale from the circuit level (and even below) through the black box level and on up through the system level. These stochastic systems are systems with random as well as deterministic features. Such a system often has the following character: it has a finite number of states (or modes) and at any time is in one of these states; it is subject to external events "input" events which tend to induce changes of state; it is the source of events, the occurrence of these "output" events being dependent on the current state and the current input event. A necessary background in finite-state, discrete-time Markov chains is first presented. Then the stochastic chain is formulated and, as an illustration, applied to a rather complex though not untypical problem, that of evaluating the worth of two alternative aircraft navigation systems. Following this practically based example, an entropy analysis is worked out. The information theory notion of entropy is used to measure the randomness of the sets of events constituting inputs and outputs of stochastic chains. Also, methods of matrix analysis are developed; these methods provide tools for framing solutions to the canonical equations of discrete-time variable and continuous-time variable stochastic chains. Solutions are developed not only for the general case, but also for important special cases. Digital computer solution methods are outlined too, and are illustrated by two-state examples. The formulation of continuous-variable stochastic chains, and the derivation of solution forms and outlining of computer solution techniques completes the treatment of single stochastic chains. The rest of the thesis extends the model: networks of stochastic chains are formulated and applied. Such networks can be applied to stochastic analysis problems of potentially arbitrary complexity; indeed, without such networks, stochastic chain analysis would be limited to systems possessing only a relatively few states (or modes) of operation. Finally, three particular application areas are explored: reliability of electronic equipments (briefly); and simulation analysis and probabilistic logics (both of these latter in considerable detail). In each area, stochastic chains used in the network context can provide potent means for analyzing complex and, in many cases, previously intractable problems.
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