Dependability and sensitivity analysis of multi-phase systems using Markov chains

This dissertation presents a new modular solution to the fault tree analysis of non-repairable multi-phase systems. The modular solution uses a combination of approaches: Binary Decision Diagram (BDD) to solve static modules and Markov chains to solve dynamic modules. Multi-phase systems are systems that are subject to operation in several phases. The system structure, failure and recovery processes, and success criteria can change with each phase. Multi-phase systems may be composed of both static and dynamic subsystems in different phases. Although it is not possible to model dynamic behavior with combinatorial methods, it is possible to divide some multi-phase systems into their static and dynamic subsystems and solve each of them independently and then combine the results for the solution of the entire system. We present a simple yet powerful modular approach for combining the dynamic and static reliability analysis approach in this work. Algorithms are also provided in this dissertation for modularization and integration of the modular solution.; However, our modular approach is not a “panacea” for all fault tolerant systems. The sub-modules of a practical system may be still too large to be solved or even the whole system may not be able to be modularized. Markov chain based approaches are thus used for solving such dynamic systems. The problem with Markov chain based approaches is that the size of the Markov model expands exponentially with an increase in the size of the system, and therefore it is computationally intensive to solve. In this work we adopt a new failure distance based bounding concept to our dynamic fault tree analysis to solve this largeness problem with the development of a method to compute lower bound for failure distance from the dynamic fault tree constructors and a modular approach for computation of the lower bounds for failure distance for a modularized dynamic fault tree. In this dissertation, we also generalize the bounding methodology from single phase systems analysis to multi-phase systems analysis.; In a reliability model of a fault tolerant system, reliability analysis of a computer-based system tells only part of the story. It is useful to identify the components or subsystems which contribute the most to system unreliability. The identification will help the system designer and analysts to improve the system reliability. To accomplish this work requires sensitivity analysis of the reliability results. We present a modular technique for evaluating sensitivity measure as well as the different sensitivity solutions using the BDD and Markov chain approach. The sensitivity analysis for multi-phase systems is also studied in this paper. The sensitivity analysis and multi-phase reliability measure methodology have been implemented into Galileo, a software package for reliability analysis of complex computer-based systems.; Finally, after a summary of major contributions of this work, possible research problems on multi-phase systems and coverage modeling using modular approach and failure distance based bounding method are suggested as direction for future work.