Uncertainty Propagation through Software Dependability Models

Stochastic models are often employed to study dependability of critical systems and assess various hardware and software fault-tolerance techniques. These models take into account the randomness in the events of interest (aleatory uncertainty) and are generally solved at fixed parameter values. However, the parameter values themselves are determined from a finite number of observations and hence have uncertainty associated with them (epistemic uncertainty). This paper discusses methods for computing the uncertainty in output metrics of dependability models, due to epistemic uncertainties in the model input parameters. Methods for epistemic uncertainty propagation through dependability models of varying complexity are presented with illustrative examples. The distribution, variance and expectation of model output, due to epistemic uncertainty in model input parameters are derived and analyzed to understand their limiting behavior.