Effect of Uncertainty in Prior Knowledge on Test Planning for a Brake Caliper using the Probability of Test Success

SUMMARY & CONCLUSIONSIn order to demonstrate a product’s reliability requirement, it is necessary to plan efficient tests that are firstly capable of demonstrating this requirement and, secondly, have a minimum sample size and conserve as many resources as possible. The concept of the Probability of Test Success [1], [2] is a highly suitable assessment method in this regard. In addition to the α error (type-I error) of the test, it also allows the β error (type-II error) to be considered, therefore enabling test assessment using the statistical power. Since statistical power can only be calculated for a certain effect size, prior knowledge is required for planning tests. In existing concepts, prior knowledge has been assumed to comprise scalar values of the parameters of a failure distribution. In reality, however, this prior knowledge is always associated with uncertainty. The aim of this paper is to outline an approach for incorporating this uncertainty into test planning and to demonstrate how it affects planning. For this purpose, tests are planned for a brake caliper from a commercial vehicle’s brake system. The prior knowledge stems from prior end-of-life (EoL) tests.The studies show that the uncertainty of prior knowledge (implemented in the form of a bootstrap Monte Carlo simulation) can be effectively taken into account when calculating the Probability of Test Success. For the brake caliper, tests with failures are compared to tests without failures (or with only a few failures) to demonstrate reliability. There is a clear disadvantage when using tests without failures, although considering uncertainty makes this even more pronounced and generally leads to a reduced Probability of Test Success. This serves to emphasize how the uncertainty of prior knowledge should be taken into account in reliability-test planning. Otherwise, a test might be selected that does not have the desired properties and—in the worst-case scenario—will not demonstrate the reliability requirement, which would incur significant additional effort in testing.In general, there are two very common reasons for reliability testing, the first of which is estimating failure distribution. The second is demonstrating the reliability requirement. The former is usually planned as a test with failures; an end-of-life test [3]. The latter is usually planned as a test without failures; a "success run" (SR) test [3], [4]. The approach presented here is novel in the sense that all possible test types can be considered for the reliability demonstration and are compared objectively. In addition, it can be seen that the EoL test often has a clear advantage over the SR test, even for the sole purpose of demonstrating reliability, while still allowing for an estimate of the failure distribution. The concept of using the Probability of Test Success and assessing all available test types and configurations enables the reliability engineer to gain a holistic view of planning for reliability-demonstration tests and makes for a very efficient test with minimal risk.