In traditional methods for reliability analysis, one complex system is often considered as being composed by some subsystems in series. Usually, the failure of any subsystem would be supposed to lead to the failure of the entire system. However, some subsystems' lifetimes are long enough and even never fail during the life cycle of the entire system. Moreover, such subsystems' lifetimes will not be influenced equally under different circumstances. In practice, such interferences will affect the model's accuracy, but it is seldom considered in traditional analysis.

To address these shortcomings, this paper presents a new approach to do reliability analysis for complex systems. Here a certain fraction of the subsystems is defined as a "cure fraction" under the consideration that such subsystems' lifetimes are long enough and even never fail during the life cycle of the entire system.

By introducing environmental covariates and the joint power prior, the proposed model is developed within the Bayesian survival analysis framework, and thus the problem for censored (or truncated) data in reliability tests can be resolved. In addition, a Markov chain Monte Carlo computational scheme is implemented and a numeric example is discussed to demonstrate the proposed model