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Cloud service-based applications are subject to reliability critical problem,as the reliability of the application relies on both the failed states and the probabilities of the failures.Classically,reliability analysis approaches are lack of estimating unknown failure rate and non-exponentially distributed failure times.We propose a new framework for analyzing the reliability.The method is mainly decomposed in four successive steps:a non-Makovian stochastic Petri net (NMSPN) model which describes the failure behavior of underlying applications,a software reliability growth model (SRGM) which estimates the failure data of each basic service,a reachability graph which discoveries all the failure sequences,and a computation procedure which computes the occurrences of non-exponential failures.We assess and validate our method by conducting experiment on an actual application.The results demonstrate that the method is competitive compared to the existing approaches for reliability analysis,while providing a better reliability.This result is helpful to the managers in optimizing the overall quality of the cloud service-based application.