The standard VDI 2048 Part 1 explains the basics of a procedure which enables the user to subject process and acceptance tests to direct quality control and to determine the probability of promised characteristics being fulfilled. This enables the user to be informed about the true state of the plant with the lowest possible degree of uncertainty. This standard provides examples with a practical orientation dealing with the determination of covariances, provides help in programming and, with the aid of a practical example, shows how the procedure is applied. The retrofit example clearly demonstrates the necessity of taking covariances into consideration if results with a high statistical certainty are to be obtained. It is included on the enclosed CD-ROM in form of a demonstration program.