HS model had the lowest mean RMSE. In Section 5.1, HS model showed lower accuracy than type 1 and type 5 Prophet and Arima, but the effect of hierarchical information pooling of HS model was significant when applying new data that was not learned. HS model showed lower RMSE than Arima in all types. Prophet showed lower RMSE in type 4 than HS model, but did not show much difference. 5.2.2. New engine type Robust estimation is possible even when forecasting the failure rate of ship with unforseen engine type; information on engine archetype is stored in hyperparameters of layer1 with which forecast can be made. In other words, the resulting \(\overset{\overline{}}{\alpha_{0}}\ \) and\(\overset{\overline{}}{w_{0}}\ \) value of a prefit, B-spline fit on averaged failure rate, are used for\(\overset{\overline{}}{\alpha_{s}}\ \)and\(\overset{\overline{}}{w_{s}}\ \)from equation 1. Fig. 6, 7, and 8 show the prediction results of HS and comparative models. Commonly, the black dots are the location of the test set data. Small red dots are the location of the train data. The green lines of HS model are the prediction line of each ship engine, the red lines are the prediction line of each engine type, and the blue line is the engine archetype prediction line. The blue line of Prophet and ARIMA is the prediction line of the whole life cycle and corresponds to the archetype prediction line of the HS model. In the figures, y-axis is expressed as scaled values due to data privacy. The test for new engine type data has the following meaning. As technology evolves, the new engine type will replace the previous engine types. Or, depending on the purpose, you may need to introduce a new engine type that has not been used before. In this case, you can refer to similar types of engine type or engine archetype trend for prediction. In this section, we confirmed that HS performed well when only the information on engine archetype could be referenced. The prediction situation in this section is notable because it is the most difficult but necessary real situation. The accuracy was compared with Prophet and Arima. The result is shown in Table 4. In all new types, the HS model had a lower RMSE than the comparative model. In the case of type 6, it is located in the section of 10 to 20 years with the smallest number of train data. The HS model predicts relatively accurately by pooling information between layers even when the number of data is small.
Table 4. Test set data RMSE (New ship engine which engine type was not trained)