A proper evaluation of the performance of a system over a specified time horizon must take into consideration the magnitudes of fluctuations in performance level over the time horizon. This paper presents a model to study the cumulative performance of a system over the time period [0,T] when performance fluctuations, whether caused by changes in the internal state of the system or by external factors such as traffic overloads, are reflected by changes in both the mean and variance of the metric being used to assess the system performance. It is assumed that the shifts in the mean and variance of the performance metric occur at epochs which follow a homogeneous Poisson process. The mean and variance of a cumulative performance function are computed in closed form. A performance index, essentially a signal-to-noise ratio, is introduced as a composite measure to account for both the mean and standard deviation of the cumulative performance function. A generalization of this index is given to deal with the case when several performance metrics must be considered simultaneously. The application of the model is illustrated through actual data on packet loss in the Access Grid (AG). The model and ideas of this paper may be useful in performance evaluation of a variety of systems such as computer networks and manufacturing systems.