A method is proposed for assessing the quality of nondestructive testing and the technical condition of tanks and vessels used in petrochemical industries, depending on the methods of nondestructive testing employed in technical diagnostics. The probability of revealing a defect was used as a criterion when assessing the quality of technical diagnostics. Estimates are given for the probability of detecting a delamination in the vessel-body wall material of different area using various schemes of applying the basic methods of nondestructive testing. It is shown that the acoustic-emission method makes it possible to significantly increase the probability of detecting a delamination in the equipment wall without increasing the scope of work by virtue of local methods of nondestructive testing. A positive effect is achieved through the use of acoustic-emission testing data (the location maps and hazard levels of acoustic-emission sources) at the stage of planning the procedure of nondestructive testing during technical diagnostics of equipment.