On computing signatures of coherent systems

It is difficult to compute the signature of a coherent system with a large number of components. This paper derives two basic formulas for computing the signature of a system which can be decomposed into two subsystems (modules). As an immediate application, we obtain the formula for computing the signature of systemwise redundancy in terms of the signatures of the original system and the backup one. The formula for computing the signature of a componentwise redundancy system is also derived. Some examples are given to illustrate the power of the main results.