Checkpoints are widely used to improve the performance of computer systems and programs inthe presence of failures, and they significantly reduce the overall cost of running a program, if the program or the underlying system, are subject to failures. Thus application level checkpointing has been proposed for programs which may execute on platforms which are prone to failures, and also to reduce the execution time of programs which are prone to internal failures. This paper develops a mathematical model to estimate the average execution time of a program in the presence of failures, without and with application level checkpointing, and we use it to predict the optimum interval number of instructions which should be executed between the placement of successive heckpoints. The case of programs with loops and nested loops is also discussed. The results are illustrated with several numerical examples.