A probabilistic extension of the refinement calculus has been successfully applied in the design of safety-critical systems. The approach is based on a firm mathematical foundation within which the reasoning about correctness and behavior of the system under construction is carried out. The framework allows us also to obtain a quantitative assessment of the attributes of system dependability. In this paper we present an extension of our main design technique - refinement - the so-called parameterized refinement. The purpose of the extension is to create a technique which facilitates refinement of a system in such a way that the dependability of the implementation would be maximal. We mostly focus on the reliability aspect. The parameterized refinement resolves the problem of how to build more reliable systems by incorporating statistical information about a controlled environment and reliabilities of system components in the development process. We illustrate this by a case study - the development of a state monitoring system.