Walsh函数在组合测试中的应用

Applied Walsh Function in Combinatorial Testing

实际软件系统非常复杂,有很多因素会影响系统的正常运行.组合测试可以对这些因素及其相互作用所引发的软件缺陷进行检测.该文在组合测试基本模型的基础上,引入Walsh函数,建立了组合测试Walsh函数模型.模型给出基于Walsh的测试用例模式的定义以及理论缺陷函数和实际缺陷函数的定义;引入Walsh模式变换概念,并利用Walsh函数的离散形式有效地计算测试用例模式的平均缺陷率.最后基于模式平均缺陷率的大小,补充附加测试用例进行重新测试,从而迅速将故障原因锁定在很小的范围内,为软件的调试和测试工作提供更方便、更有价值的线索和参考.

Software is a very complex system in practice, and may be affected by many factors. Combinatorial testing could detect the faults triggered by the factors and their interactions. Based on the studies of basic models of combinatorial testing techniques, we introduce Walsh function in the field of combinatorial testing and establish an analysis model of Walsh schema. This model presents the concepts about the test case schema, the theoretic defect function （a function defined on the test suite） and the actual defect function~ through the Walsh schema transform and the discrete form of the Walsh function, we can effectively compute the average defect rate of the test case schema. Finally, based on this average defect rate, it then can conclude that the errors must be in a very small range through analyzing the test cases and retesting with some complementary test cases. So it can provide the very efficient and valuable guidance for the debugging and testing of software.