**4. Approach Description for Maintenance Costs Evaluation**

As just described in the previous paragraph, the model for maintenance costs will be based on the scheduled preventive maintenance and the MTBM (Mean Time Between Maintenance) value [22]. Settled the ship type, the first step is to identify some different design configurations that satisfy the main owner requests, like speed, range, operational profiles, maneuverability performance, environment, and efficiency performance.


$$\text{MTBM}' = \text{MTBM} - \frac{1}{\text{h}\_{\text{T}}} \cdot \left[ \sum\_{i} \text{h}\_{\text{ACT}\_{i}} \cdot \frac{\left( \text{P}\_{\text{T}\_{i}} - \text{P}\_{\text{ACT}\_{i}} \right)}{\text{P}\_{\text{T}\_{i}}} \right] \cdot \text{MTBM} \tag{4}$$

where MTBM' is the new corrected MTBM, the actual value; MTBM is the original manufacturer value; hACT is the number of actual off-design working hours; hT is the number of total actual working hours in one year; PT is the power corresponding to the optimal working point; PACT is the actual power; *i* is the operational scenario considered, like navigation at 13 kn or navigation at 8 kn, etc. This type of formulation can be applied to the diesel engines for the generation of propulsion.

If PACT and PT are equal, the engine works at its best and MTBM = MTBM'. The same result is obtained if hACT = 0, i.e., the engine is in its best working point. We have assumed that the formulation has an application domain from 20% to 50% of MCR engines power: if an engine works above the 50% of its MCR, the corrective formula is not applied; at the same time for MCR less of 20%, the formula is not recommended.


The tool provides all the information needed to have a general overview of maintenance-related costs over the ship life cycle, with graphical and tabular results. Figure 2 summarizes the maintenance framework where WBS systems and subsystems are written in lines, and the higher is the level of detail, more lines are required.

The columns report (from left to right) a system or subsystem description; the maintenance task description (there could be more tasks for the same WBS voice); the number of same items; the effective MTBM, expressed in working hours or years and corrected with the previous formula; the number of hours dedicated to the task; the number of men required to do the particular task; the man costs; the spares cost (if a spare part is required); the total maintenance task costs; the times that the task is repeated during ship life cycle; the LCC value.


**Figure 3.** Maintenance tool structure overview. LCC: Life Cycle Costing; MTBM: Mean Time Between Maintenance; WBS: Work Breakdown Structure.

The prediction model is structured to have the WBS, maintenance tasks, number of items, MTBM, man-hours, number of man, and man costs as input data. The model automatically calculates the

MTBM', the total cost of each maintenance tasks, the times each action has to be performed during the ship life, and the costs (indicated as LCC on the right in Figure 3).

During the early design stage, the definition of the ship operational profile is very relevant and has a strong influence on the propulsion system typology. In turn, the propulsion system strongly affects the ships final building cost and the costs linked to operational activity during the whole ship life [16]. From that described above, the LCPA tool has been further enhanced to evaluate the best configuration among some proposed alternative propulsion layouts. Due to the great number of systems and sub-systems installed, the complex connections between them, and the massive amount of required information, it is necessary to further reduce the domain of investigation in this development phase. This work aimed to develop a tool to predict the maintenance costs during the design stage, also when the information available is not so detailed. The intention was to develop a solid and adaptable starting point that could be improved during further interactions or directly customized from the designers themselves over their needs. Once the results of the costs derived from the maintenance tool are inserted in the main LCPA tool, the designer can provide a first attempt to quantify the total ship costs, not only related to building costs but also related to the operating costs. This type of assessment could permit to offer a better and complete overview of the product in a constructive discussion with the customer.

This methodology has been applied to a reference vessel, described in Section 5, to improve its propulsion system. The alternatives systems have been described one by one in Section 6 and are directly compared in Section 7 to identify the best solution.
