Why combinatorial testing works: Analyzing minimal failure-causing schemas in logic expressions

Combinatorial testing technique has been applied on Boolean-specification testing. Previous results indicated that it performed well to detect faults in Boolean expressions. This paper aims to investigate the reason why combinatorial testing works in Boolean-specification testing, which was always omitted previously. We design experiment to get the minimal failure-causing schemas for 19129 faults, which could be classified into 10 fault classes, of 20 Boolean expressions that extracted from TCAS system. By analyzing the number and strengths of minimal failure-causing schemas for each fault, the low bound of fault-detecting probability of τ-way combinatorial test suite for Boolean-specification testing are calculated. Computational results could explain the effectiveness of combinatorial testing technique in Boolean-specification testing.