The accelerated Degradation testing (ADT) experiments are important technical methods in reliability studies. Different type of accelerating degradation models have developed with the time and can be used in different types of situations. However, it has become necessary for the manager to test how many no of units should be tested at a particular stress level so that the cost of testing is less. Such experiments allow the experimenter to run the test units at higher-than-usual stress conditions in order to secure failures more quickly.The Inverse Gaussian process is flexible in incorporating random effects and explanatory variables. The different types of models based on IG process are random drift model, random volatility model and random drift- volatility model. In this paper we have considered random drift model for the study onstochastic degradation models for simple step-stress model using inverse Gaussian process observed in degradation problems.