  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.
