Table 5. Euclidean distances
Conclusions
We have proposed using HS to develop a hierarchical model for forecasting failure rates. This approach shines especially when the data have unbalanced category and structured characteristic. We demonstrated the applicability of the model using a real-world dataset of failure rate data from Naval ships and compared it with previous methods. Through these comparisons, we confirmed that the prediction performance of our novel model in the given dataset was greatly improved. Moreover, we have shown how qualitative knowledge, such as the belonging to the same series or construction era, could be incorporated into the model; this approach was justified by further analyzing the relationship between each parameter. These techniques could greatly improve Naval ship management efficiency. Some improvement could be noted for further studies. First, prevention repair which may affect the failure pattern could be considered. A more advanced model that incorporates the probability of failure after the prevention repair is needed to design a model. Second is convergence and evaluation measures. There were few instances with low E-BMI and effective sample size, n_eff. Improving the model in terms of higher E-BMI and n_eff measures would result in a better fit of the model. Thirdly, due to substantial operational differences between combat and non-combat ships, only combat ships are used in this paper. However, if the differences could be incorporated in the further models, by using categorical variables, a more accurate model could be possible based on a larger amount of data. The proposed model can contribute greatly to the following areas. First, failure rate prediction could be used as a quantitative reference when establishing a maintenance policy. Proper maintenance not only improves the availability and mission completion rates but also reduces the budget by reducing unnecessary maintenance. Second, from a broader perspective, the predicted failure trend can be a qualitative reference for designing the optimal life cycle of a ship. For instance, based on our results, the failure rate increases dramatically as the ship becomes senile. Therefore optimal retirement period could be decided by balancing the maintenance and construction cost. The proposed model can contribute greatly to the following areas. First, failure rate prediction could be used as a quantitative reference when establishing a maintenance policy. Proper maintenance not only improves the availability and mission completion rates but also reduces the budget by reducing unnecessary maintenance. Second, from a broader perspective, the predicted failure trend can be a qualitative reference for designing the optimal life cycle of a ship. For instance, based on our results, the failure rate increases dramatically as the ship becomes senile. Therefore optimal retirement period could be decided by balancing the maintenance and construction cost.
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