Cascade chart (NDI interval reliability)
This name was first introduced by Dr. Alberto W Mello in his work "Reliability prediction for structures under cyclic loads and recurring inspections".
Materials subject to cyclic loads, as shown in the graph on the right, may form and propagate cracks over time due to fatigue.
The non-destructive inspection (NDI) technique must have a high probability of detecting a crack in the material.
The main purpose of using NDI techniques is to comb the surface of a material for small cracks that could affect the integrity of the entire structure.
For example, visual inspection is the least reliable method because the human eye can only resolve and identify cracks on the order of millimeters.
This number can be used in a Weibull-like distribution to map the probability of detection as a function of crack size.
In any case, it is important to have a maintenance plan that allows multiple opportunities to find a crack that may be small and difficult to access.
A cascade chart is an alternative way from the traditional damage tolerance analysis (DTA) methodology for determining a reliable inspection interval.
The probability of detection (POD), a function of the NDI method, accessibility, and crack size, can be modeled by the equation below.
α, and λ, on the other hand, are parameters related to the chosen NDI method that determine the shape of the probability curve.
Based on typical variation of material properties, the constants C and m in the equation below can be varied to represent different crack growth rates.
The probability of detection distribution curve for a chosen NDI method is superimposed to the crack growth curve, and the inspection interval is systematically changed to compute the cumulative probability of detection for a crack growing from the minimum to the critical size.
The simulation is repeated several times, and a distribution of inspection interval versus structural reliability can be formed.
As it is clear in the chart, the scatter in NDI decreases as the intervals are reduced and reliability is increased.
Several sources of uncertainties can be included in the simulations, such as variation in material properties, the machining quality, the inspection methods, and accessibility of the crack.
Hopefully, using this process, the inspection interval will lead to a higher percentage of cracks being detected before failure, ensuring greater flight safety.
A final important observation is that improving the NDI method can increase the number of flight hours needed before re-inspection while maintaining a relatively low risk level.
