Large-scale simulations often use Krylov methods to solve sparse systems of equations in high performance computing environments. To mitigate the latency associated with global communication, algebraically equivalent pipelined versions of Krylov methods have been introduced. The increasing complexity of HPC computing environments has introduced many sources of run-to-run variability at different levels of HPC systems. In this work, we develop a performance model and study the impact of operating system noise, machine variance, and other factors on Krylov and pipelined Krylov method execution. We collect fine-grained data that shows the influence of variability on Krylov and pipelined Krylov methods. To succinctly describe the execution performance, we employ stochastic models based on the distribution of iteration times of each method. We test the models with collected data and suggest ways to improve and expand them in order to make a prior performance estimates.