It is difficult to determine a curve of the probability of crack detection (POD) with a high confidence level

since the traditional procedures require very large sample sizes.A new method of determining the POD curves is presented.The method requires only upwards of 30 independent inspections for determining a POD curve.The formulas of one sided lower confidence limits of the POD curves and of POD/CL crack sizes are also established by means of Fisher information matrix.In order to predict and prevent mechanical failure through probabilistic damage tolerance design and analysis

the POD curves for multiple independent inspections have been studied

and a important concept of controlling lives and a method of the optimum independent inspection times are presented.This method can control the largest size of the cracks missed at inspections with high POD and confidence level

and the largest size of the missed cracks is used as the initial crack size for calculating the crack growth life of the structure in damage tolerance design.Thus the crack growth lives and inspection intervals of structures can be controlled to some extent.The method can also raise the crack detection probability and avoid the accidents caused by the missed cracks.