Accelerated degradation model based on geometric Liu process

Through evaluating stress levels, Accelerated Degradation Testing (ADT) can obtain degradation data in a limited period of time and then use these data for reliability evaluations. However, because of the high price of the test items or the test equipment, the sample size used in ADT is usually small, which causes a lack of knowledge on recognizing the population and then lead to the epistemic uncertainty. The small sample problem makes the probability theory based models, which need large samples, not appropriate any more. To address this problem, based on the uncertain theory, this paper uses the general geometric Liu process to construct an uncertain acceleration degradation model, and gives the corresponding statistical analysis method with objective measures. A carbon-film resistors case is used to illustrate the proposed methodology, and discussions are conducted on the sensitivity analysis of the proposed methodology to the sample sizes. Results show that the proposed methodology is a suitable choice for the reliability evaluations of ADT data under small sample situations.