We propose a method for conducting mean-variance assessment of the cost and risk of a given unit commitment schedule with respect to thermal generating unit outages, assuming deterministic net load to be satisfied over a specified time horizon. By repeating the sequence of load levels and the unit commitment schedule cyclically over an extended time horizon, the linear dependence of the mean and variance of the dispatch cost on the length of that horizon can be exploited.  A simplifying assumption motivated by the $N-1$ security criterion allows the dispatch cost, considering stochastic forced outages, to be modeled as a renewal reward process.  A limit for the time average and an asymptotic approximation for the variance of the cost can then be computed quickly. Numerical results for an IEEE test system show that the approach provides a usefully accurate assessment of risk.