Inference on an adaptive accelerated life test with application to smart-grid data-Acquisition-devices

An accelerated life test (ALT) is often well planned to yield the most statistical information given limited test resources. Nevertheless, ALT planning requires rough estimates of the model parameters as an input, called planning values. The discrepancy between the planning values and the true values may result in insufficient or even no failures at the low-stress level, making the subsequent data analysis difficult. Motivated by the need in the ALTs of data acquisition devices used in smart grids, an adaptive ALT scheme is proposed. The key idea is based on the observation that, when the product reliability is underestimated during the ALT design phase, it is unlikely to observe failures at the early stage of the test. Therefore, the low-stress level should be elevated to protect against insufficient failures. Under this adaptive ALT framework, order statistics techniques are used to derive the likelihood function by assuming a general loglocation-scale distribution for the product lifetime. Confidence intervals for the parameters are constructed based on the large-sample approximation as well as the accelerated bootstrap method. A simulation study is conducted to demonstrate the advantages of the adaptive ALT compared with the simple constant-stress ALT. Its application is illustrated using the motivating example from smart grids.