A algebraic system, Test Algebra (TA), identifies faults in combinatorial testing for SaaS (Software-as-a-Service) applications. SaaS is a software delivery model that involves composition, deployment, and execution of mission application on cloud platforms. Testing SaaS applications is challenging because a large number of configurations needs to be tested. Faulty configurations should be identified and corrected before the delivery of SaaS applications. TA proposes an effective way to reuse existing test results to identify test results of candidate configurations. The TA also defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. This paper proposes one MapReduce design of TA concurrent execution in a cloud environment. The optimization of TA analysis is discussed. The proposed solutions are simulated using Hadoop in a cloud environment.