AbstractA production system operates at a speed which is a stationary stochastic process. Given the routine control point, the actual accumulated production observed at that point and the deterministic rate of demand, the decision-maker determines the timing of the next control point. The problem is applied to semiautomated production processes where the advancement of the process cannot be measured or viewed continuously, and the process has to be controlled in discrete points by the decision-maker. Since the cost of performing a single control is relatively high, the control should be carried out as rarely as possible but it also has to ensure a preset confidence probability of achieving production output no less than that required. Formulae for determining the next control point for an arbitrary distribution function of the stationary process with a certain autocorrelation function are presented. They depend on the status of the system (shortage or surplus), the relation between the rate of demand and the mean value of the speed, the variance of the speed, and on the confidence level 1-α. A practical numerical example from the mining industry will be given.