The advent of software components in the safety critical systems of nuclear power plant has introduced new challenges for software professionals to provide increased software reliability. Several proposals have been proposed for ensuring software reliability in different phases of software development life cycle. The present article is a novel attempt in providing an exhaustive survey of software reliability models for their applicability on safety critical systems of nuclear power plants. Our systematic review shows that none of the proposals for ensuring software reliability are applicable on such systems. The issues and challenges are discussed, and a software reliability model for safety critical system of nuclear power plants is proposed.