Competing Risks Model for Step-stress Experiments under Lagged Effects with Masked Data

Abstract

In the step-stress tests, the most common model is Nelson’s Cumulative Exposure Model, where the hazard function is discontinued at the change stress level changing point. However, the continuous change hazard function in the step-stress tests is more accordance with actual situation. We addressed this issue by incorporating a lag period in the model, resulting in a continuous hazard function with linearly increasing hazard in the lag period. Also, when a test unit fails, there are often several risk factors associated the cause of failure, which is commonly referred to as competing risks. If we can get the failure time information, but cannot identity the exactly cause, we call this type of data as masked data. In this paper, we deal the parameter estimation of the masked data in competing risks under simple step-stress circumstance with lagged efiects. We apply the maximum likelihood approach via the expectation-maximization algorithm for the parameters estimation, and use the bootstrap method for the parameters confldence interval estimation. To verify the validity of the model, we illustrated it by a numerical example.