Analysis of destructive degradation tests for a product with random degradation initiation time

Most research on degradation models and analyses focuses on nondestructive degradation test data. In practice, destructive tests are often conducted to gain insights into the changes of the physical properties of products or materials over time. Such tests sometimes provide more reliable degradation information than nondestructive tests that may only yield indirect degradation measures, such as temperature, amount of metal particles, and vibration. However, an obvious drawback of destructive tests is that only one measurement can be obtained from each specimen. Moreover, some products start degrading only after a random degradation initiation time that is often not even observable in destructive degradation tests (DDTs). Such a degradation-free period adds another dimension of complexity in modeling DDT data. In this paper, we develop two delayed-degradation models based on DDT data to evaluate the reliability of a product with an exponentially distributed degradation initiation time. For homogeneous and heterogeneous populations, fixed-effects and random-effects Gamma processes are considered, respectively, in modeling the actual degradation of units after degradation initiation. A maximum likelihood method as well as an expectation-maximization algorithm is developed to estimate the model parameters, and bootstrap methods are used to obtain the confidence intervals of the interested reliability indices. Numerical examples demonstrate that the proposed models and estimation methods are effective in analyzing DDT involving random degradation initiation times.