An economical balance is sought between the cost of testing and the expectation of loss due to accepting an insufficiently reliable product or rejecting a sufficiently reliable one, the desired reliability being very high. When the articles to be tested are classifiable into just two groups, satisfactory or defective, use is made of Poisson approximations to obtain “optimum” sequential tests as well as optimum fixed size tests. The results are presented in charts. When the articles to be tested are classifiable according to some physical measurement whose underlying distribution is supposed to be normal, but is otherwise unknown, the optimization is based on previously obtained solutions using normal approximations. Examples are given.