A group single sampling attribute plan to attain a given strength

A single sampling attribute plan cannot be designed satisfying the given strength exactly. It is suggested that a group consisting of atmost three single sampling plans be operated at random with certain proportions so that the group as a whole attains the given strength exactly. The problem of choosing atmost three plans with the proportion of times they should be operated with minimum average sample size is shown to be a linear programming problem. An example with solution by simplex method is given.