A. N. GOLODNIKOV, P. S. KNOPOV and V. A. PEPELYAEV ESTIMATION OF RELIABILITY PARAMETERS UNDER INCOMPLETE PRIMARY INFORMATION ABSTRACT. We consider the procedure for small-sample estimation of reliability parameters. The main shortcomings of the classical methods and the Bayesian approach are analyzed. Models that find robust Bayesian estimates are proposed. The sensitivity of the Bayesian estimates to the choice of the prior distribution functions is investigated using models that find upper and lower bounds. The proposed models reduce to optimization problems in the space of distribution functions. KEY WORDS: Reliability parameters, Bayesian procedures, Incomplete information 1. INTRODUCTION One of the main stages in the existing procedure for risk esti- mation in environmentally hazardous systems involves the determination of parameters that characterize equipment reli- ability. These parameters include, for instance, the failure rate and the probability of failure at the instant when the equipment is needed. The accuracy of the parameter estimates obtained at this stage largely affects the end result, i.e., the risk assessment of the entire environmentally hazardous system. The popular statistical methods used for reliability estimation rely on two main approaches: the methods of classical sampling theory and Bayesian procedures. The classical approach pro- duces a satisfactory estimate if sufficient primary information on equipment failures is available. Sampling methods, however, are inadequate for the analysis of small samples, which are often all that we have for estimating the parameters of high-reliability equipment. In nuclear power stations, for instance, there are Theory and Decision (2005) 57: 331–344 Ó Springer 2005 DOI 10.1007/s11238-005-3217-9