This short paper describes a numerical method for optimising the conservative confidence bound on the reliability of a system based on tests of its individual components. This is an alternative to the algorithmic approaches identified in Bishop and Povyakalo (RESS 2020). For a given maximum number of component tests, the numerical method can derive an optimal test plan for any arbitrary system structure. The optimisation method is based on linear programming which is more efficient that the alternative integer programming. In addition, the optimisation process need only be performed once for any given system structure as the solution can be re-used to compute an optimal integer test plan for a different maximum number of component tests. This approach might have broader application to other optimisation problems that are normally implemented using integer programming methods.