Traditionally, reliability models of component-based software systems compute the point estimate of system reliability by plugging point estimates of unknown parameters into the model. These models discard the uncertainty of the parameters, that is, do not attempt to answer the question how parameters uncertainties affect the estimates of system reliability. In this paper we focus on uncertainty analysis in software reliability based on method of moments. In particular, we present a generalization of our earlier work that allows us to consider the uncertainty in the operational profile (i.e., the way software is used) in addition to the uncertainty in components failure behavior (i.e., component reliabilities) considered earlier. The method of moments is an approximate analytical method that allows us to generate system reliability moments based on (1) the knowledge of software architecture reflected in the expression of system reliability as a function of component reliabilities and frequencies of control transfer between components, (2) estimates of the moments of components reliabilities, and (3) estimates of the moments of probabilities of control transfer between components. Further, we apply the method of moments on two case studies and discuss its advantages and disadvantages.