Master of Science / Department of Computing and Information Sciences / David A. Gustafson / The calculation of reliability based on running test cases refers to the probability of the software not generating faulty output consequent to the testing process. The metric used to measure this reliability is referred in terms of E(Θ) value. The concept of E(Θ) gives precise formulae to calculate the probability of failure of software after testing, debug or operational. This report aims at extending the functionalities of E(Θ) into the realm of multiple faults spread across multiple sub-domains. This generalization involves introduction of a new set of formulae for E(Θ) calculation which can account for faults spread over both single as well as multiple sub-domains in a code. The validity of the formulae is verified by matching the obtained theoretical results against the empirical data generated from running a test case simulator. The report further examines the possibility of an upper bound calculation on the derived formulae and its possible ramifications.