Letncomponents of some type be subjected to a number (k) of tests : if a component passes all the tests it is regarded as reliable. The costs of administering each test to a component are known as well as the 2kprobabilities that a component will pass some tests and fail the others. There areK! ways in which the test can be ordered and the problem of finding the optimum, the most cost-effective sequencing of these tests was discussed in Berger and Gerstenfeld (1972). By the application of branch -and-bound technique the method of solving this problem can be simplified.