Extreme (X-)Testing With Binary Data and Applications to Reliability Demonstration

Reliability demonstration techniques are used to formally verify that the reliability of a product meets a specified target with a certain degree of confidence. When the reliability target to be demonstrated is very high (close to one), traditional reliability demonstration plans require extremely large sample sizes or have low power. One solution to this problem is to inflate the failure probability by testing products under extreme conditions so that they are more likely to fail. It is sufficient then to demonstrate a lower reliability target which can be mapped back to the required reliability under standard conditions. This paper develops a general framework for this type of extreme testing, or “X-testing”, with binary data. The effects of X-testing on sample size and power of reliability demonstration plans are discussed. Properties of various X-transforms are studied with respect to zero-failure plans, fixed sample size plans, and fixed power plans. Conditions under which X-transforms lead to inadmissible or uniformly efficient tests are obtained. X-testing is similar in spirit to accelerated testing as both methods are intended to induce failures, but there are some key differences. Several applications, in addition to reliability demonstration, are used to illustrate the general usefulness of the approach.