Introduction

Forecasting failure rate is important as it serves as a standard for preventive measure, inventory management. Both over and underestimation of failure are detrimental to the system. Underestimation can lead to mission failure due to failure, overestimation can lead to wasted budget and reduced operational efficiency due to excessive spare part purchases. Therefore taking account of features of failure data into the model is important. Two characteristics of failure rate data, unbalanced category and sharing structure, are the main motivation for this paper and we propose hierarchical spline model for improvement. First, unbalanced category refers to the fact that collected data corresponding to each age are unbalanced for each category; product type, for example. Second, is sharing structure. In our case of predicting the failure rate of an engine of each ship, as engines are shared among ships, ships with the same type of engine display similar failure rate patterns. The underlying process also supports the empirical results, as the same engine types share design patterns and are made from the same factory. Hierarchical model provides a systemic structure to improve both unbalanced category and sharing characteristic of data. In our problem setting, even the failure rate of an age period where data of a certain ship engine is unavailable could be forecasted as parameters could be borrowed from other types of ships and engines. For this purpose, we have constructed our three-layer model as the following: a root layer that accounts for the core characteristics of an engine, i.e. engine archetype, a second layer which corresponds to each type of an engine, and lastly, the final layer that explains the specific characteristics of each ship. The proposed model has additional advantages in terms of forecasting the failure of new engine types. Republic of Korea (ROK) Navy battle ship evlove continuously; for example, FF (Fate Frigate) class have been replaced by FFG (Fast Frigate Guided-missile). Forecasting the failure rates of a new battle ship is clueless, but necessary. Most existing time series models such as ARIMA or ETS(exponential smoothing) model struggles in situation where no quantitative data exist. However, in hierachical model it is possible to constuct the outline of the failure function based on the prior qualitative information. For instance, as we will elaborate in section 5, engines constructed in similar era show similar patterns. Therefore, information on which era the unforeseen engine was made could be utilized to forecast its failure rates. The proposed model has additional advantages in terms of forecasting the failure of new engine types. ROK Navy battleship evolve continuously; for example, FF (Fate Frigate) class has been replaced by FFG (Fast Frigate Guided-missile). Forecasting the failure rates of a new battleship is clueless, but necessary. Most existing time series models such as ARIMA or ETS (exponential smoothing) model struggles in situations where no quantitative data exist. However, in hierachical model it is possible to construct the outline of the failure function based on the prior qualitative information. For instance, as we will elaborate in section 5, engines constructed in a similar era show similar patterns. Therefore, information on which era the unforeseen engine was made could be utilized to forecast its failure rates. The main contribution of this paper lies in applying hierarchical spline (HS) model to address unbalanced category and sharing structure of failure data from ROK Navy. Compared to the previous models, the proposed model not only improves overall forecast accuracy but also is capable of forecasting failure rates for categories with scarce data robustly. Moreover, the hypothetical similarity between each category can be tested and proved using our model; this enables users to utilize the qualitative knowledge on the unforeseen, ships with new engines for example, for forecasting. These results, when used as a reference for maintenance policy and budget allocation, could contribute greatly to the Navy’s operating system. However, this model is not limited to Naval domain. When it comes to forecasting failure rates, the circumstances where data are hierarchical, unbalanced, or insufficient are common and therefore, our model is widely applicable. For example, mechanical equipment consists of a number of parts. The generator, which is a part of the wind turbine, is composed of parts such as a motor and a transformer (Scheu, M. N. et al., 2019) in a hierarchical structure. Using the HS model, it is also possible to predict the failure of equipment components in a hierarchical structure. The remainder of this paper consists of five sections. Section 2 introduces the background behind failure forecasting in marine as well as the key concepts upon which the HS model is based. Section 3 introduces HS model and explains the advantage especially in terms of characteristics of the real data. In section 4, data obtained from the ROK Naval ships is introduced and experimental models are described and compared. Section 5 contains an analysis of the experimental models, and lastly, conclusions are presented in section 6.