Orthogonal arrays are intricate combinatorial structures that are useful in various fields including statistics. Their application to the efficient planning of experiments has been of substantial interest in recent years. The problem of examining the existence of orthogonal arrays is a challenging one and the well-known Bose-Bush bound plays a fundamental role in this context. This bound will be revisited in the present talk from a new perspective. It will be seen that an elementary statistical idea can facilitate the understanding of this bound and even entail some improvement over it. Some related open problems will be discussed.