The fault detection capability of metamorphic testing (MT) largely depends on the “quality” of metamorphic relations (MRs)[3]. Since MRs are often identified based on human judgment and, hence, the identification task may not be properly performed. Thus, systematic MR generation has long been an important research issue in MT. In addition, MT researchers are concerned about the cost-effectiveness of MT, in view of the extra overhead associated with executing the program with follow-up test cases. This gives rise to the issue of reducing the test cost of MT. MR composition [1, 2] can address both of these issues, by automatically composing existing MRs to form new ones and thereby reducing the number of follow-up test cases. Although this approach is intuitively sound, previous studies on MR composition have empirically shown that the fault detection capability of MRs may be reduced after composition [1, 2]. This has inspired us to conduct theoretical and empirical analyses to identify what characteristics components MRs should possess so that their corresponding composite MR has at least the same fault detection capability as the component MRs do.

Our analysis has found some characteristics of the component MRs, which are defined in terms of the bijectivity/injectivity of these component MRs’ input and output mappings. As such, these characteristics are easily verified by a tester. The existence of these characteristics in component MRs guarantees that the fault detection capability will not be jeopardized after MR composition. The validity of our findings has been formally proved, and their practicality has been checked via an empirical study. To promote the applicability of our results, we have also formulated convenient yet effective guidelines to help a tester determine whether or not MR composition should be used.