In this paper, estimation of the accelerated life testing (ALT) for the stress model in multiple case is considered. Maximum likelihood estimation is employed to obtain the estimated parameters of the multiple-stress model by a maximum likelihood approach. A Bayesian estimation procedure is proposed to estimate the parameters of the multiple-stress model. Estimation methods are considered under a progressively type-Ⅱ hybrid censoring scheme with generalized inverted exponential distribution. Different criteria are discussed to determine the optimal design of the progressively type-Ⅱ hybrid censoring scheme for the multiple-stress model. A simulation study is conducted to obtain results for the maximum likelihood and Bayesian estimates of the parameters of the multiple-stress model. Real data application involving the breakdown voltage of insulating oil is introduced to analyze the performance of the multiple-stress model under progressively type-Ⅱ hybrid censoring scheme with generalized inverted exponential distribution.

Because of modern technology, product reliability has increased, making it more challenging to evaluate products in real-world settings and raising the cost of gathering sufficient data about a product's lifetime. Instead of using stress to accelerate failures, the most practical way to solve this problem is to use accelerated life tests, in which test units are subjected to varying degrees of stress. This paper deals with the analysis of stress-strength reliability when the strength variable has changed m levels at predetermined times. It is common for the observed failure time data of items to be partially unavailable in numerous reliability and life-testing studies. In statistical analyses where data is censored, lowering the time and expense involved is vital. Maximum likelihood estimation when the stress and strength variables follow the Gompertz distribution was introduced under type I censoring data. The bootstrap confidence intervals were deduced for stress-strength reliability under m levels of strength variable and applying the Gompertz distribution to model time. A simulation study was introduced to find the maximum likelihood estimates, bootstrapping, and credible intervals for stress-strength reliability. Real data was presented to show the application of the model in real life.