Test-Algebra-Based Fault Location Analysis for the Concurrent Combinatorial Testing

A new algebraic system, test algebra (<formula><tex>$\mathsf{TA}$</tex></formula>), is proposed for identifying faults in combinatorial testing for software-as-a-service (SaaS) applications. In the context of cloud computing, SaaS is a new software delivery model, in which mission-critical applications are composed, deployed, and executed on cloud platforms. Testing SaaS applications is challenging because new applications need to be tested once they are composed, and prior to their deployment. A composition of components providing services yields a configuration providing an SaaS application. While individual components in the configuration may have been thoroughly tested, faults still arise due to interactions among the components composed, making the configuration faulty. When there are <formula><tex>$k$</tex></formula> components, combinatorial testing algorithms can be used to identify faulty interactions with <formula><tex>$t$</tex></formula> or fewer components, for some threshold <formula><tex>$2 \le t \le k$</tex></formula> on the size of interactions considered. In general, these methods do not identify specific faults, but rather indicate the presence or absence of some faults. To identify specific faults, an adaptive testing regime repeatedly constructs and tests configurations in order to determine, for each interaction of interest, whether it is faulty or not. In order to perform such testing in a loosely coupled distributed environment such as the cloud, it is imperative that testing results can be combined from many different servers. The <formula><tex>$\mathsf{TA}$</tex></formula> defines rules to permit results to be combined, and to identify the faulty interactions. Using the <formula><tex>$\mathsf{TA}$</tex></formula>, configurations can be tested concurrently on different servers and in any order. The <formula><tex>$\mathsf{TA}$</tex></formula> always keeps the high reduction rate of potential faulty configurations in fault location analysis.