Test coverage (TC) is one of the typical measures of software testing effectiveness. It aims at identifying how thoroughly a test suite exercises a given program. Though a number of functions have been proposed to describe the dependency of TC on time, none of them can be used in case when the analytical expressions for at least some of their components are unknown or imperfectly known. The paper considers an alternative approach to deriving test coverage model, which operates only on the upper and the lower bounds on the components of TC functions. The core step of the novel methodology is transforming the initial data via interval-valued (imprecise) probability technique. This obtained imprecise TC description is incorporated into software reliability growth model which can be used for assessment of software reliability and failure prognostics. The final algorithm for solving the problem involves the ideas from optimal control theory applied to searching for the estimates of reliability maximum and minimum values. The proposed procedure is illustrated with numerical example.