The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi’s method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (necessity), and designs which involve variables each of which has a range of values any of which might be used (possibility). Tuning parameters, as a part of the design process, are also introduced into Taguchi’s method. The method is also extended to solve design problems with constraints, invoking the methods of constrained optimization. Finally, the Taguchi method uses a factorial method to search the design space, with a confined definition of an optimal solution. This is compared with other methods of searching the design space and their definition of an optimal solution.