Previous theoretical studies on the effectiveness of partition testing and random testing have assumed that test cases are selected with replacement. Although this assumption has been well known to be less realistic, it has still been used in previous theoretical work because it renders the analyses more tractable. This paper presents a theoretical investigation aimed at comparing the effectiveness when test cases are selected with and without replacement, and exploring the relationships between these two scenarios. We propose a new effectiveness metric for software testing, namely the expected number of distinct failures detected, to re-examine existing partition testing strategies.postprin
