Confidence interval of lifetime distribution using bootstrap method

Lifetime estimation is significant in engineering asset management. However, the estimate of lifetime or failure time could be misleading as it may not reveal the real value. Therefore, confidence intervals need to be built to quantify the prediction uncertainty. For the Gamma process, which is a commonly used method for lifetime estimation, the conventional confidence interval construction methods do not perform well. This paper adopts bootstrap methods to build confidence intervals of lifetime distribution when the Gamma process is used. Three bootstrap methods, i.e. bootstrap percentile, bootstrap-t and bootstrap bias corrected & accelerated (BCa), are utilized and investigated. These methods are first applied to the basic Gamma process and further to the Gamma process which considers random effects. Moreover, bootstrap calibration is conducted to assess the coverage probability of the confidence intervals built by these bootstrap methods. Applications to the fatigue crack growth data are carried out as a case study. The results show that the BCa method is recommended for generating confidence intervals for Gamma processes in this application.