We introduce a formula for computing system survival signatures by the means of merging survival signatures of multiple subsystems. The algorithm extends previous results for survival signatures on merging systems with no common components to systems with common components. It also extends existing results on merging dependent systems for calculating Samaniego's system signatures to survival signatures. Apart from these trivial extensions, we also introduce a novel decomposition method which allows us to decouple the dependencies among subsystems according to a wider class of events which may lead to savings of computational resources.
The survival signatures can be equivalently represented by the counting signatures. We present our results for computing them. The survival signatures can then be obtained by simple point-wise division.