Large scale applications running on new computing plat- forms with thousands of processors have to face with reliability prob- lems. The failure of a single processor will cause the entire execution to fail. Most existing approaches to guarantee reliable executions are based on fault tolerance mechanisms. Coordinated checkpointing is one of the most popular technique to deal with failures in such platforms. This work presents a new model of coordinated Checkpoint/Restart mechanism for several types of computing platforms. The model is parametrized by the process failure distribution, the cost to save a global consistent state of processes and the number of computational resources. Through mathe- matical analysis of reliability, we apply this new model to compute the optimal interval between checkpoint dates in order to minimize the av- erage completion time. Its main feature is that it is independent from the type of the failure law which makes it very exible. We show that such a model may be used to reduce the checkpoint rate up to 20% in same cases and up to factor 4 the total overhead in same cases. Finally, we report some experiments based on simulations for random failure distributions corresponding to the two most popular laws, namely, the Poisson\'s process and Weibull's law.