On a progressively censored competing risks data from Gompertz distribution

We study a competing risks model using Gompertz distribution under progressive Type-II censoring when probability distributions of failure causes are identically distributed with common scale and different shape parameters. Maximum likelihood estimates (MLEs) of these parameters are obtained and their uniqueness and existence behavior are also discussed. The asymptotic intervals are derived from the observed Fisher information matrix. We compare the performance of all the estimators numerically using simulations. Analysis of a real data set is presented as well. We further determine optimal censoring scheme using expected Fisher information matrix. The design parameters are selected based on suitable measures like cost-based and variance-based criteria functions. Finally, we discuss single and multi-objective optimization approaches to find optimal censoring schemes.