Abstract
Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two bootstrap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity.