large numbers of cycles endured by the rotating component, an undetectable crack may grow to a critical length in a single flight and before the aircraft lands, result in a catastrophic failure that regular maintenance could not have prevented. Damage tolerance analysis In ensuring the continued safe operation of the damage tolerant structure, inspection schedules are devised. This schedule is based on many criteria, including: assumed initial damaged condition of the structure stresses in the structure (both fatigue and operational maximum stresses) that cause crack growth from the damaged condition geometry of the material which intensifies or reduces the stresses on the crack tip ability of the material to withstand cracking due to stresses in the expected environment largest crack size that the structure can endure before catastrophic failure likelihood that a particular inspection method will reveal a crack acceptable level of risk that a certain structure will be completely failed expected duration after manufacture until a detectable crack will form assumption of failure in adjacent components which may have the effect of changing stresses in the structure of interest These factors affect how long the structure may operate normally in the damaged condition before one or more inspection intervals has the opportunity to discover the damaged state and effect a repair. The interval between inspections must be selected with a certain minimum safety, and also must balance the expense of the inspections, the weight penalty of lowering fatigue stresses, and the opportunity costs associated with a structure being out of service for maintenance. Non-destructive inspections Manufacturers and operators of aircraft, trains, and civil engineering structures like bridges have a financial interest in ensuring that the inspection schedule is as cost-efficient as possible. In the example of aircraft, because these structures are often revenue producing, there is an opportunity cost associated with the maintenance of the aircraft (lost ticket revenue), in addition to the cost of maintenance itself. Thus, this maintenance is desired to be performed infrequently, even when such increased intervals cause increased complexity and cost to the overhaul. Crack growth, as shown by fracture mechanics, is exponential in nature; meaning that the crack growth rate is a function of an exponent of the current crack size (see Paris' law). This means that only the largest cracks influence the overall strength of a structure; small internal damages do not necessarily decrease the strength. A desire for infrequent inspection intervals,