Statistical flowgraph models have proven useful for analysis and modeling of complex systems viewed as multistate processes that lead to outcomes such as degraded operation or failure. This article provides an engineering-oriented introduction to statistical flowgraph models: system representation, setting up a flowgraph model, parameter estimation, solution of the model (using either a frequentist or Bayesian approach), and interpretation of model outputs. The method is illustrated with a model for piping reliability in a nuclear power plant, and compared with alternative solution methods.