This study discusses the point and interval estimations of two-parameter Gompertz distribution under partially accelerated life tests with Type-II censoring. Also, the study considers the optimal design problem in the case of time step-stress model. The maximum likelihood estimators and approximate confidence intervals of the model parameters are derived. Also, optimum test plans for the time step-stress life tests are developed. For illustration, a simulation study is provided.

Key words: Gompertz distribution, partially accelerated life test, maximum likelihood estimation, Newton-Raphson method, fisher information matrix, Monte Carlo simulation, type-II censoring, optimal design, generalized asymptotic variance.