One of the problems of risk analysis of complex engineering systems is the uncertainty of initial information about the time and damage associated with occurrence and development of the risk situation. The paper proposes a methodology and procedure for constructing a risk tree, loading it with initial data, calculating the corresponding characteristics: the distributions of time to reach the intermediate and main risk events and of associated with them damages, as well as their moments. Methodology involves the construction of the most dangerous path of risk situation development with respect to different criteria as well as analysis the sensitivity of risk characteristics to the initial information. The proposed approach is applied to a model of an automated system for remote monitoring of underwater gas pipeline. The proposed methodology and its implementation on a real-world example constitute the novelty of the work.