Cost-risk optimization of nondestructive inspection level

This paper develops a quantitative methodology for determining the nondestructive inspection (NDI) level that will result in a minimum cost product considering both type one inspection errors, acceptance of defective material units, and type two inspection errors, rejection of sound material units. This methodology represents an advance over fracture mechanics — nondestructive inspection (FM-NDI) design systems that do not consider type two inspection errors or the preinspection material quality. The inputs required for the methodology developed in this paper are (1) the rejection probability as a function of inspection size and imperfection size, (2) the flaw frequency (FF), as a function of imperfection size, (3) the probability of failure given the material unit contains an imperfection of a given size as a function of that given size, (4) the manufacturing cost per material unit, (5) the inspection cost per material unit, and (6) the average cost per failure including indirect costs. Four methods are identified for determining the flaw-frequency and three methods are identified for determining the conditional failure probability (one of these methods is probabilistic fracture mechanics). Methods for determining the rejection probability are discussed elsewhere. The NDI-FF methodology can have significant impact when the cost of failures represents a significant fraction of the manufacturing costs, or when a significant fraction of the components are being rejected by the inspection.