5.2. Linear regression and optimization
If the results of DT simulations can be analyzed and optimized, the system can be improved. Each simulation result of the four models was linearly regressed. Compared to non-linear, it is easier to understand the relationship between variables. Depending on the purpose, multi-regression or other statistical methods may be applied. Fig. 10 shows the results of linear regression of operational availability (Ao) and probability of critical failure (Probability_CF). Their relationship is related to the reliability of the mission. This is because the success rate of the mission is determined depending on which policy is adopted after setting the target Ao. If Probability_CF is small at the target Ao line, it can be said that the policy has a high mission success rate. As shown in Fig. 10, in the case of PFM_NRP and FFM_NRP, Probability_CF is 0 at target Ao. In the regression with a higher dimension, FFM_NRP had a lower Probability_CF at Ao. The relationship between PFM_FRP and FFM_FRP is noteworthy. FFM_FRP is the basis of CBM. Since the maintenance time is flexibly determined, normal failures accumulated in the ship can be effectively repaired. However, if FFM_FRP is applied, Probability_CF is higher than the current maintenance policy (PFM_FRP) in target Ao. In other words, it has the advantage of being able to effectively repair failures, but the probability of mission failure during naval operation is higher. If the navy pushes forward to apply CBM, it can be seen that not only FFM but also NRP should be promoted at the same time. In the case of this research model, 1.2 billion simulations were required for each model in order to confirm all the necessary scenarios in ROK Navy. In the performance of the computer used in the study (Intel Core i7 2.6Ghz, 16GB DDR4 RAM), about 5 seconds was consumed for one simulation. Linear regression can be used as a method to solve time-consuming problems in large-scale simulations such as DT. This is possible by constructing an optimization objective equation and performing arithmetic calculations using a linear regression equation between the independent variable and the dependent variables constituting the objective equation. The Navy needs a policy with high operational availability, low mission failure rate (probability of critical failure), and low total lifecycle cost. Expression (1) is equivalent to expressing their relationship.\(\frac{\text{Operational\ availability}}{Probability\ of\ critical\ failure\times\ Life\ cycle\ cost}\)(1) It took about 16 minutes to check the optimization results of the models with the objective of Equation (1). The method using the linear regression equation has the advantage of being able to quickly check the rough results, although the accuracy will be lower than that of simulating all scenarios or calculating through non-linear relational equations.