Sequential Testing of Series-Parallel Systems of Small Depth

We consider the problem of testing sequentially the components of a multi-component system, when testing the components is costly. We consider a polynomial time testing policy for series-parallel systems, and prove, generalising earlier results that it is cost-minimal in the average case sense, for two sub-families of series-parallel systems. We also demonstrate via examples that neither this algorithm nor some of its improved versions are optimal for general series-parallel systems, disproving some published claims.