Simultaneous testing of multicharacteristic components

We consider optimal testing policies for multiple components, each with multiple characteristics. The problem ends when all components have failed a test or one component passes every test. Previous literature demonstrated the optimality of simple ratio rules for sequencing when testing components and their characteristics one-at-a-time. We consider the possibility of testing components simultaneously, while still testing their characteristics one-at-a-time. We show that the ratio rule is no longer necessarily optimal and construct a heuristic with a performance guarantee.