Timing the control point under the exponential stationary process

In semiautomated production processes, the advancement of the process cannot be measured or viewed continuously. Therefore, it has to be controlled by the decision-maker in discrete points. The cost of performing a single control is relatively expensive and, therefore, control should be carried out as rarely as possible, on condition that a pregiven probability of achieving production output no less than that required is ensured. Formulae are presented for determining the next control point, where the speed of the production process at each moment behaves as an exponential distribution function of a stationary process with a certain autocorrelation function. The formulae depend on the status of the system (shortage or surplus), the relation between the rate of demand and the mean value of the speed, and the confidence level 1-α. A comparison between the exponential stationary process and the Gaussian process is given.