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Computing systems are of growing importance because of their wide use in many areas including those in safety-critical systems. This book describes the basic models and approaches to the reliability analysis of such systems. An extensive review is provided and models are categorized into different types. Some Markov models are extended to the analysis of some specific computing systems such as combined software and hardware, imperfect debugging processes, failure correlation, multi-state systems, heterogeneous subsystems, etc. One of the aims of the presentation is that based on the sound analysis and simplicity of the approaches, the use of Markov models can be better implemented in the computing system reliability.