Cost-based optimal relation between inspection time and assessment time for random fatigue crack growth

Optimal inspection time for random fatigue crack growth is theoretically investigated based upon cost-minimization, using a diffusive crack growth model. The optimal inspection time is defined so as to minimize the expected total cost expended up to the assessment time, at which the effect of an inspection is quantified. Assuming that (i) only one inspection is done up to the assessment time, and (ii) the component is immediately replaced if a crack is detected by the inspection, we formulate the expected total cost by the use of the diffusive crack growth model, where randomness associated with the material inhomogeneity, the initial crack length and crack-detection is taken into analysis. Through numerical calculations, we derive the optimal inspection time as well as the optimal expected cost. Finally, we perform parameter sensitivity analyses, and discuss the optimal selection of the assessment time.