Alexander Grundler’s research while affiliated with Bosch and other places

Empirical life tests are used for reliability demonstration and determination of the actual reliability of the product. Therefore, engineers are faced with the challenge of selecting the most suitable test strategy out of the possible many and also the optimal parameter setting, e.g. sample size, in order to realize reliability demonstration with limited costs, time and with their available testing resources. It becomes even more challenging due to the stochastic nature of failure times and necessary cost and time being dependent on those. The considerations and guidelines in this paper are intended to simplify this process. Even simple products can fail due to several causes and mechanisms and usually have several components and subsystems. Therefore, this paper provides test planning options for single critical failure mechanisms as well as for systems with multiple failure mechanisms. For this purpose, the Probability of Test Success (Statistical Power of a life test) is used as a central, objective assessment metric. It is capable of indicating the probability of a successful reliability demonstration of a test and thus allows, for example, to answer the question of the required sample size for failure-based tests. The main planning resource is prior knowledge, which is mandatory due to the stochastic lifetime, in order to provide estimates for the Probability of Test Success at all. Therefore, it is also shown how to deal with uncertain prior knowledge and how the underlying information can additionally be used to increase the Probability of Test Success using Bayes’ theorem. The guidelines show how the most efficient test can be identified in the individual case and for individual boundary conditions.

Planning reliability demonstration tests is particularly complex if end-of-life tests are used instead of standard success run tests. In addition to the factors of cost and time, the probability of test success can be used to select the optimal test strategy. This has already been considered for a single-stage load in several papers. In real applications single stage loads are not applied. Using single stage loads also leads to ignoring the changing confidence level of the life model due to the placement of the test load levels. Recent research now also uses operating load spectra, deriving the probability of test success for the accumulated damage of the load spectrum. Considering the influence of this operating load spectrum on the probability of test success is therefore a logical step. To determine if there is an influence and how different parameters change the influence a simulation study with a wide parameter space is executed and analyzed. The study shows an influence where different parameters can affect the achievable probability of test success. This happens due to the interaction of the operating loads of the spectrum with the confidence level of the life model influenced by the test levels and test specimen.

Statistical power analyses are used in the design of experiments to determine the required number of specimens, and thus the expenditure, of a test. Commonly, when analyzing and planning life tests of technical products, only the confidence level is taken into account for assessing uncertainty. However, due to the sampling error, the confidence interval estimation varies from test to test; therefore, the number of specimens needed to yield a successful reliability demonstration cannot be derived by this. In this paper, a procedure is presented that facilitates the integration of statistical power analysis into reliability demonstration test planning. The Probability of Test Success is introduced as a metric in order to place the statistical power in the context of life test planning of technical products. It contains the information concerning the probability that a life test is capable of demonstrating a required lifetime, reliability, and confidence. In turn, it enables the assessment and comparison of various life test types, such as success run, non-censored, and censored life tests. The main results are four calculation methods for the Probability of Test Success for various test scenarios: a general method which is capable of dealing with all possible scenarios, a calculation method mimicking the actual test procedure, and two analytic approaches for failure-free and failure-based tests which make use of the central limit theorem and asymptotic properties of several statistics, and therefore simplify the effort involved in planning life tests. The calculation methods are compared and their respective advantages and disadvantages worked out; furthermore, the scenarios in which each method is to be preferred are illustrated. The applicability of the developed procedure for planning reliability demonstration tests using the Probability of Test Success is additionally illustrated by a case study.

Over the past decades, product development cycles have become shorter and shorter, with reliability requirements increasing while budgets for testing have decreased. To select a test that makes the best use of resources (cost and time) for reliability requirement with a sufficient level of confidence, a simulation is performed. In previous work by Herzig et al. [3] and Grundler et al. [4] the concept of Probability of Test Success (𝑃𝑡𝑠) introduced by Dazer et al. [1] was applied. To improve the applicability of the test planning procedure, a load spectrum rather than a single field load level is now to be evaluated. This is necessary because many products are not subjected to a single field load, but to fluctuating conditions that have natural causes such as the seasons, time of day or individual users. Finally, a case study is evaluated for individual parameters of a test scenario to minimize test time and cost while maximizing 𝑃𝑡𝑠.