**3. Risk Assessment and Inspection Interval Optimization**

This section provides the results of the risk assessment and optimization of inspection interval for a composite aircraft tail wing structure. In the first stage of risk assessment, it is highly desirable to develop an efficient response surface that requires fewer FE executions. The composite crack propagation curve response surface was generated for both the sensitive parameters for the damage range of 2 to 10 mm. Thirty samples generated from the LHS were used for the generation of a total of nine response surfaces, as shown in Figure 13a. The average value of the mean square error (R2) of the nine response surfaces was 0.9987, with a minimum R<sup>2</sup> value of 0.9962. It was confirmed that the response surface

model satisfied the minimum standard value of R2 ≥ 0.990 set in this study. The present study dealt with the reliability evaluation of the structure using an efficient adaptive response-surface-based MCS technique. The analysis should consider all the uncertainties required for accurate damage growth modeling and risk assessment. For this purpose, damage growth simulation was performed using an MCS. The crack propagation curves using response surface modeling were accurately simulated compared with FE simulations, as represented in Figure 13b.

**Figure 13.** (**a**) Response surface generation using Latin hypercube sampling design and (**b**) the simulation response surface based on FEA simulations.

After the development of the response surface, we estimated the single flight probability of failure (SFPOF) assuming the structure was non-repairable. For the FRCPs, nondestructive inspection (NDI) was insufficient to detect the cracks that can propagate to complete failure of the structure. Therefore, it is essential to minimize the risk by computing the minimum inspection cycle. For this purpose, SFPOF was proposed in 1980 to assess the risk of aircraft failure [30]. It provides the probability of failure during one flight. To evaluate the risk, the criteria may vary depending on the operating environment conditions. The US Department of Defense proposed that a structural risk assessment should be performed on a component-by-component basis, and defined the limits on *SFPOF* of between 10−<sup>7</sup> and 10−<sup>5</sup> for each component. According to the suggested range, if *SFPOF* > 10−5, the component is unacceptable for operation. For 10−<sup>5</sup> > *SFPOF* > 10<sup>−</sup>7, the structure requires repair and modification to ensure long-term operation. For *SFPOF* < 10<sup>−</sup>7, the structure is safe for long-term operation. In this study, *SFPOF* defined the amount of damage reached in the component with respect to the total number of simulations, as shown in Equation (5):

$$SFPOF = P(a \ge a\_{critical}) = \frac{N\_{critical}}{N\_{simulation}} \tag{5}$$

where *Ncritical* is the number of simulations exceeding the critical damage size and *Nsimulation* is the total number of simulations.

In this study, *SFPOF* was computed at 3000 FHs. At 3000 FHs, the damage distribution is calculated. The probability was computed for the scenario that the damage was greater than the critical crack size, which was 8 mm. Using the above process, the SFPOF was calculated for the total number of FH, as shown in Figure 14.

**Figure 14.** Single flight probability of failure calculation at 3000 FHs.

For a critical component, such as an aircraft tail wing, the common practice is to perform multiple inspections. The reason for repeated inspections is that the inspections are never perfect. There is always the possibility of misclassification. Therefore, repeated inspections are likely to reduce the inspection cost. For the determination of an optimal inspection plan, an optimal number of repeated inspections is needed. The time between repeated inspections can be computed using the following equation:

$$T\_{repact} = \frac{T\_{design} - T\_{initial}}{N\_{Inposition} + 1} \tag{6}$$

where *Tinital* is the initial inspection cycle, *Tdesign* is the operating life, and *NInspection* is the number of repeated inspections. In this study, the service life of the tail wing structure considered was 3000 FHs, with the first inspection cycle at 200 FHs. Figure 15 shows the calculation of repeat inspection cycles with respect to the number of repeated inspections.

**Figure 15.** Number of repeated inspections with respect to the number of inspection plans.

The criteria for determining the optimal inspection cycle in this study was based on the US Airforce standard of risk assessment matrix [31]. In the event of an accident, the severity level is divided into four levels based on the type of result, component damage, etc. The Risk Assessment Code, or Hazard Risk Index, is a risk level that is calculated by combining the severity and probability of occurrence, as shown in Table 3. A high risk constitutes the first−fifth level range. The serious risk of component failure falls in the sixth–ninth level range, the medium risk falls in the 10th–17th level, whereas the low risk is in the 18th−20th level range.


**Table 3.** US Airforce airworthiness risk assessment matrix [31].

The overall process implemented in this study for determining the optimal inspection interval is divided into three steps, as shown in Figure 16:

Step #1. Determination of the severity category

In the event of an accident caused by a defined major failure mode, the severity level was determined after predicting the consequences.

Step #2. Calculation of the probability of failure (probability level)

The probability of failure was calculated by computing the SFPOF for each flight time.

#### Step #3. Risk assessment code

Steps #1 and #2 were combined to calculate the risk. If the calculated risk was less than the target level, step #2 was repeated after modifying the inspection cycle combination.

In the case example of an aircraft tail wing, the first step was computed by assuming the severity level to be critical. In the second step, the assumed operating life was 3000 flight times. After setting it equal to a critical value, the SFPOF was calculated for each FH until the end of the operating life, and the maximum SFPOF was set as the reference value. The RAC from the maximum probability of failure and severity level was calculated. If the target risk level was a medium risk: RAC 10−17, then the combination of the least number of repeated inspections among the combinations of inspection cycles that satisfied RAC 10−17 is selected. In this example, the optimal inspection cycle was calculated when the number of repeated inspections was six and fell within the medium risk level, as shown in Figure 17.

**Figure 16.** Process of determining the optimal inspection cycle.

**Figure 17.** Selection of optimized inspection from the RAC-vs.-severity-level curve.
