The Problem of Testing for the Fraction of Defectives

A balance is sought between (1) the cost of testing for reliability and (2) the risks, because of limiting the testing, of either accepting an insufficiently reliable product or rejecting a sufficiently reliable one. The latter risk is generally less serious than the former. With a suitably defined pay-off function, “optimum” parameters are obtained both for a fixed-size test and a sequential test of the type introduced by Wald. The mathematical treatment is valid except for very high reliabilities. Modifications are discussed for (i) an optimum sequential test when the pay-off function includes some uncertainty as to what is meant by sufficiently reliable, and (ii) an optimum sequential test between two rival products.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.