Competing risks in the step-stress model with lagged effects
In reliability and survival analysis, accelerated tests are often used to reduce the duration of the test. In this dissertation, we consider the class of step-stress tests where items are subject to an initial stress level which is subsequently increased at pre-determined times during the exposure. The stress factor may represent temperature, drug dosage, or voltage. The most common model used for step-stress tests is Nelson's Cumulative Exposure Model, originally proposed by Sedyakin. A significant drawback of the model is that the underlying hazard function is discontinuous at points where the stress is changed. The Cumulative Risk Model discussed by Kannan, Kundu, and Balakrishnan addressed this issue by incorporating a lag period in the model, resulting in a continuous hazard function.
In many applications, there are several competing causes of failure. We generalize the stepstress model of Kannan et al. to include two competing causes. The first model assumes constant hazards at both the initial and elevated stress levels. The second model assumes a monotone hazard function for the two stress levels based on the Weibull distribution. In the lag period, we assume the hazard is linearly increasing. We obtain the maximum likelihood estimators of the unknown parameters and construct the observed Fisher information matrices.
To evaluate the performance of the estimators, a Monte Carlo simulation study is performed for different sample sizes and parameter values. The bias and mean squared error of the estimators are computed as well as confidence intervals and coverage probabilities using large sample theory and bootstrap methods.