This study presents developed algorithm for assessment and updating estimates of parameters in the mathematical models of non-stationary processes (for instance, system ageing model, dynamic system models and so on) with respect of prior information and new obtained observations. Proposed algorithm for updating estimates of random parameters is based on modified application of Bayesian approach (BA). Developed algorithm was applied for Ignalina NPP Unit 2 RBMK-1500 reactor's closure of the gas-gap between the pressure tubes and the graphite bore probabilistic analysis.