Modelling structural coverage and the number of failure occurrences with non-homogeneous Markov chains

Most software reliability growth models specify the expected number of failures experienced as a function of testing effort or calendar time. However, there are approaches to model the development of intermediate factors driving failure occurrences. This paper starts out with presenting a model framework consisting of four consecutive relationships. It is shown that a differential equation representing this framework is a generalization of several finite failures category models. The relationships between the number of test cases executed and expected structural coverage, and between expected structural coverage and the expected number of failure occurrences are then explored further. A non-homogeneous Markov model allowing for partial redundancy in sampling code constructs is developed. The model bridges the gap between setups related to operational testing and systematic testing, respectively. Two extensions of the model considering the development of the number of failure occurrences are discussed. The paper concludes with showing that the extended models fit into the structure of the differential equation presented at the beginning, which permits further interpretation.