Risk-based life-cycle optimal dry-docking inspection of corroding ship hull tankers

Highlights

• Investigate the economically optimal dry-docking time of corroding ships under uncertainty.

• Use the minimum expected cost criterion to determine the optimal dry-docking time.

• Incorporate the condition-based ship structural renewal policy in the maintenance planning.

• Consider both the maintenance cost and failure consequence of ships.

Abstract

The performance of the ship hull deteriorates randomly over time under corrosion attacks. To ensure the safe operation of a ship, dry-docking inspections are carried out on a regular basis to inspect, recoat, and renew structural members. The convention “at least two inspections every five years”, implemented in the shipping industry, is empirically determined without much numerical evidence. Considering the expensive cost of dry-docking inspections, it is crucial to study the optimal inspection interval in the presence of uncertainty. This paper proposes a risk-based maintenance decision-making framework for ships to address the optimal dry-docking inspection. The minimum expected cost rule is used to explore the economically optimal inspection interval. Monte Carlo simulations are employed to obtain the probability distribution of the life-cycle cost. The costs considered include the cost of dry-docking and member renewal as well as monetary consequences of hull failure. A ship hull is utilized to illustrate the application of the proposed framework.

Introduction

The loss of a ship has significant implications in terms of environmental impact, economic loss, and crew casualties. Metal loss corrosion is a primary concern for the safety of aging ships [1], [2]. By decreasing the modulus of the hull cross-section, growing corrosion reduces the ultimate strength against external loadings. To maintain the satisfactory integrity of the hull, ships are dry-docked for inspection at a minimum twice in a 5-year period [3]. During the inspection, the thickness of the structural members of the hull is measured using non-destructive tools (e.g., ultrasound inspection), structural renewal is performed for the critical members and new protective coatings are applied to the hull surface to protect against corrosion [4]. Dry-docking is an expensive process and accounts for the largest maintenance cost throughout the ship service life. The cost of one dry-docking can be as high as $0.2 M to $0.7 M [4]. Dry-docking can also adversely affect the flexibility of operational schedules by taking a ship out of service. It is of paramount importance to explore a cost-effective inspection schedule that allows the ship to stay longer in water while guaranteeing an acceptable level of safety.

Determining the optimal inspection is not a simple task. Various uncertainties are associated with the performance of the hull. Specifically, the bending moment induced by still water and sea waves experienced during one voyage is uncertain; the spatial variability of geometric and material properties associated with different structural members, the uncertainty associated with the prediction of bending-resistant capacity, and the stochastic corrosion growth result in the uncertain structural performance of the hull. These uncertainties need to be addressed by using reliability methods. In addition, in-service ships are maintained in compliance with the rule by International Association of Classification Societies (IACS) [5], i.e., the structural members are renewed at dry-docking if corrosion penetration depth reaches the wastage allowance. This condition-based maintenance policy should be considered in the investigation of the optimal dry-docking inspection.

The optimal maintenance strategy for the corroded ship under uncertainty has been investigated [6], [7], [8]. Sun and Guede Soares [6] studied the ship inspection schedule with an annual reliability constraint. The structural members were assumed to be renewed if the probability of corrosion depth exceeding the wastage allowance was greater than a certain value. In addition to reliability, Dong and Frangopol [7] investigated the optimal inspection of the corroded hull by incorporating the life-cycle cost, whereas the failure consequence considered only includes the loss of the ship. In the risk-based maintenance framework for ships proposed by Garbatov et al. [8], comprehensive aspects of failure outcomes are considered, including the environmental impact, the loss of the cargo and ship, and fatalities, although it was implicitly assumed that structural renewal was age-based, independent of the corroding condition of structural members.

Clearly, there is still a lack of in-depth study on the risk-informed ship maintenance considering the condition-based structural renewal policy that is consistent with realistic practice, while the application of condition-based inspection decision-making has been illustrated for pipeline systems [9], [10], [11]. This study attempts to develop a practical condition-based decision-making framework for the optimal risk-informed dry-docking inspection. The structural renewal rule by IACS is incorporated in the analysis. The probability distributions of the life-cycle cost, including the cost of dry-docking (i.e., inspection and recoating), the cost of structural renewal, and failure consequence, are computed using Monte Carlo simulation. The minimum expected life-cycle cost rule is employed as the decision-making criterion to determine the optimal inspection time interval. The remainder of the paper is structured as follows. Section 2 provides information on the life-cycle cost throughout the service life of ships. Then, the reliability assessment of corroded ships is presented in Section 3. After that, a brief introduction of structural renewal policy is given in Section 4. In Section 5, the optimal inspection schedule of a ship hull is investigated. Conclusions are presented in the last section.