A Revisit of Metrics for Test Case Prioritization Problems

For the test case prioritization problems, the average percent of faults detected (APFD) and its variant versions are widely used as metrics to evaluate prioritized test suite's efficiency of fault detection. By a revisit of metrics for test case prioritization, we observe that APFD is only available for the scenarios where all test suites under evaluation contain the same number of test cases. Such a limitation is often overlooked, and lead to incorrect results when comparing fault detection efficiency of test suites with different sizes. Moreover, APFD cannot precisely illustrate the process of fault detection in the real world. Besides the APFD, most of its variants, including the NAPFD and the APFD(CW), have similar problems. This paper points out these limitations in detail by analyzing the physical explanation of APFD series metrics formally. In order to eliminate these limitations, we propose a series of improved metrics, including the relative average percent of faults detected (RAPFD) and the relative cost-cognizant weighted average percent of faults detected (RAPFD(CW)), to evaluate the efficiency of the test suite. Furthermore, for the scenario of parallel testing, a series of metrics including the relative average percent of faults detected in parallel testing (P-RAPFD) and the relative cost-cognizant weighted average percent of faults detected in parallel testing (P-RAPFD(CW)) are proposed too. All the proposed metrics refer to both the speed of fault detection and the constraint of the testing resource. A formal analysis and some examples show that all the proposed metrics provide much more precise illustrations of the fault detection process.