State Reduction for Semi-Markov Reliability Models

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model construction and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. Automatic model generation programs have been written to help the reliability analyst produce models of complex systems. Because of the importance of these programs, the model reduction technique needs to be precise and easily implemented. This paper presents a model reduction technique called trimming that can be applied to a popular class of systems. An error bound for the trimming procedure is derived that uses readily available system parameters. The trimming procedure is precisely described and appears easy to implement in a model generation program.