Applications of the Kalman filter as a tool in univariate process monitoring and optimal control are studied. A simple Kalman filter model, the steady model, leads to estimation of the process mean by a geometric moving averge (GMA) of samples means. A gener- alization of the steady model due to J. Q. Smith (1979)('1) leads to estimation of the process variance by a GMA of sample variances. Properties of the GMA as a process monitoring tool are studied using integral equations for moments of run length distributions. Adaptive versions of each of the above estimation procedures are developed. Properties of the adaptive versions are studied via simulation;The Kalman filter is also used as a tool in stochastic control theory. A nonstandard but intuitively appealing cost structure is introduced for the optimal control problem. This structure leads to optimal policies that, unlike usual optimal control policies, are consistent with Shewhart statistical process control Philosophy; That is, process adjustment is called for only when evidence if;misadjustment is strong. Tables that allow implementation of these new policies are provided; ('1)Smith, J. Q. 1979. A generalization of the Bayesian steady forecasting model. Journal of the Royal Statistical Society, B, 41, 375-387.