Processing parameters of at least one plate-shaped object, e.g. a semiconductor device or wafer, or a flat panel display, in a processing tool are adjusted depending on which processing device out of at least one set of processing devices has been used for the semiconductor device in a preceding step. A virtual or physical tag is generated, which connects the semiconductor device identification with the processing device identification. This enables a compensation of tool-dependent effects in previous processing of a single device. An example is chemical mechanical polishing prior to lithography, where alignment marks can be deteriorated differently between CMP-units. The amount of compensation is detected and evaluated by metrology tools, which—depending on the sequence of the metrology step relative to the processing step to be adjusted—either feed-forward or feed-backward their results to the processing tool. The yield of semiconductor device production is advantageously increased.