AbstractThis article introduces a replacement life‐test procedure for the exponential failure rate: Failure‐free operation of a unit for at least tk consecutive time units is designated a “success”; the acceptance test is passed if and only if the first success is encountered before k unit failures have been recorded. Test plans are presented and the test is compared with the usual time‐truncated test and to the truncated sequential probability ratio test. It is shown that this new test has smaller expected test time than the time truncated test when the true failure rate is small relative to the null hypothesized failure rate. Consistency and unbiasedness are proved and methods for making inferences on failure rate are described.