While a first leading semiconductor wafer (11) already processed in a process appliance (1) and belonging to a batch is being measured in a microscope measuring instrument (2) in relation to values for the structure parameters 30, a second or further semiconductor wafer (12) belonging to the batch is processed in the process appliance (1). An event signal (100) reports, for example, an inspection carried out successfully of the first wafer, so that the following wafers (12) no longer need to be inspected. Using the measured results, the process parameters (31) of the process appliance (1) are automatically readjusted. Events such as maintenance work or parameter drifts in trend maps etc. are detected in control units (8 or 9) and, via the output of an event signal (102), for example in an event database (40), lead to the event-based selection of structure parameters (30′) to be measured and/or to the initiation of a leading wafer (11). Limiting-value violations (21) of at least one process parameter (31), detected by a control unit (8), are responded to by a warning signal (101) and likewise fed into the event database (40).