Optimization of inspection schedule for a surface-breaking crack subject to fatigue loading

Inspections play an essential role in the damage tolerance approach to control fatigue damage. In this paper a method is presented to optimize the cost-effectiveness of inspection scheduling for single and multiple inspections during the expected lifetime. Detailed results are given for a surface-breaking crack of depth aa in a cyclic tension field. The original crack depth is treated as a random variable with a known probability density function. The crack growth is governed by the Paris law, and the inspection technique has a known probability of detection. The component fails when the crack depth reaches a critical value acr. As a part of the damage-tolerant approach, the component is replaced only when the depth of the detected crack is larger than a pre-defined value arar. For a pre-determined number of cycles that defines the expected lifetime the optimal number of cycles for the inspection scheduling has been obtained by minimizing a total cost function. The total cost function is the sum of the cost functions for failure, component replacement and inspection. These functions have been expressed is terms of the relevant probabilities. Analytical and numerical results are given for one, two and multiple inspections. These results show the effects of the magnitude of arar, and the probability of detection (POD) of the inspection technique on the optimum schedule of inspections.