Summary: This article provides the stochastic and statistical framework to model software reliability in the presence of an operational profile. The software system is used under a randomly changing operational process so that the failure characteristics depend on the specific operation performed. The operational process describes, in a probabilistic sense, how the software is utilized by the users. The time to failure distribution for each fault is exponentially distributed with a rate that depends on the operation. As soon as a failure is experienced, the fault that caused the fault is removed immediately with certainty. We discuss several issues related to software reliability and statistical inference.