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evlove continuously; for example, FF (Fate Frigate) class have been
replaced by FFG (Fast Frigate Guided-missile).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.