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The need to mitigate downtime in marine vessels arising from propulsion system failures has led ship operating companies to devote enormous resources for research based solutions. This paper applied duration models to determine failure probabilities of shaft and gearbox systems in service boats. Using dockyard’s event history data on boat repairs and maintenance, we applied Kaplan Meier hazard and survival curves to analyse probability of failure of shaft and gearbox systems in supply, crew and tug boats. We found that average time to shaft and gearbox failure was 8.33, 5.23 and 5.21 months for tug, supply and crew boats respectively. The hazard plots however, showed that supply boats had higher probability of failure than crew boats and then tug boats in that order. Further analysis using Cox regression model showed that the boats’ shaft and gearbox system failures were significantly affected by level of lubrication oil, stress corrosion cracking and impacts on the propulsion system’s components. The paper proposes that design of maintenan ce schedules for service boats should take the following into consideration: 1) estimated survival limits or failure times of propulsion system’s shaft and gearboxes , 2) significant risk factors that affect failure mode of the propulsion system components.

The productivity of service vessels depends on good working condition of propulsion system—consisting of main engine, gearbox reduction system, propeller, propulsion shaft and bearings. Specifically, properly aligned propulsion shaft and sound gearbox systems are critical to maintaining smooth operation of a vessel’s propulsion system. Shaft and gearbox failure in propulsion system could occur at all stages of a vessel’s lifecycle and which event often impact seriously on the manoeuvrability and safety of the vessel. In addition, propulsion system component failures could lead to expensive loss of hire and disruption in vessel’s schedule of operation. Apart from commercial losses, environmental impact after an accident as a result of propulsion system failure is another concern that is becoming increasingly important and subject to inquiries from regulatory agencies and other stakeholders in the shipping industry. The factors responsible for gearbox failure and shaft misalignment in marine propulsion systems are random events. That is to say that system failure can occur without warning or opportunity for correction by operators. Consequently, various techniques have had to be developed to enable risk assessment of marine propulsion systems components and thus control downtime of vessels or their components. This paper seeks to develop a method for controlling shaft and gearbox failures in marine propulsion system using data from dockyard records.

Objectives of Study

The main objective of this study is to conduct event history analysis of shaft and gearbox systems in service boats.

The specific objectives of this study are to:

1) Estimate probability of failures in propulsion shaft and gearbox systems of service boats.

2) Compare the frequency of shaft and gearbox system failures in crew, tug and supply boats.

3) Determine significant causes of failure in shaft and gearbox systems of the boats.

This paper will be limited to analysis of failure events of shaft and gearbox systems in service boats (namely: crew, tug and supply boats).

Propulsion systems take numerous forms depending on the size and purpose of a vessel.

However, large oil tankers often have their large slow speed marine diesel engine directly coupled to the propulsion shaft, see

Smaller vessels may have multiple engines and shafts. If multiple shafts are used, then the stern tube bearing is moved forward and struts are used to support the shaft so that the propeller can be moved to a usable location without creating a non-hydrodynamic hull shape. Shaft alignment is defined by the American Bureau of Shipping (ABS) as a static condition observed at the bearings supporting the propulsion shafts [

Generally, risk in marine propulsion systems may arise from equipment failure, human error, external events and institutional error. Equipment failure—the most readily recognised hazard on ships may be categorized as either independent failure, such as loss of steering due to failure of a power pump or common cause failure, such as loss of propulsion and steering resulting from total loss of electrical power to the ship, etc. Risk from external events arises from hazards such as collision with other ships, sea state, wind and ice or other weather factors. Humans provide another source of risk to marine systems when they lack skill, are excessively fatigued, or commit sabotage. Institutional failure creates risks from poor management including inadequate training, poor communication and low morale [

Others papers on fault detection techniques were based on spectral content analysis of emitted vibration signals from rotating marine propulsion machinery. Signal processing is based on Fast Fourier Transform (FFT). The FFT converts a signal from the time domain to the frequency domain. The use of FFT also allows its spectral representation [

The above studies applied fault prediction and detection models that were based on probability models and signal processing. It was also demonstrated that marine propulsion system failure is a random phenomenon, always associated with the operating state of the system which causes are either deterioration in the components of the system and/or human associated errors. Therefore the main concern should be to maintain system performance measures such as reliability and availability to achieve high profit goals and productivity [

The data in the study were obtained from records of a commercial dockyard and covered maintenance and repair activities carried out on service boats that called for service at the dock. The Dockyard which has a floating dock, specialised in repairs and maintenance of propulsion shaft and gearbox systems. The boats in the study which comprise crew, supply and tug boats were deployed as support vessels to oil & gas activities in Nigeria’s offshore oil fields. Details of their operations included transport of personnel, oil-rig equipment, towing services, ship’s berthing and manoeuvring operations. The records contained details of ship-visits for routine maintenance or repairs following breakdowns. Thus, there were two categories of boats involved: the first category comprised of boats that were brought to the dockyard as a result of misaligned shaft or malfunctioned gearbox. The second category represented boats that were brought to the dock for routine maintenance and not as a result of failed propulsion system components. Information obtained from the skippers contacted showed that these vessels were kept on tight work schedules. In most cases, they were operated in excess of eight hours daily and maintenance policy was not strictly followed. However, the data compiled contained only vessels that had made repeated visits to the yard for a period of two years. Other details included frequency of ship-visits/tows to the yard for repairs, type of service boats involved, type of propulsion system’s failure, cause of failure, dates the boats called at dock for service (repairs/maintenance) and time boats sailed after service at the dock. From the records, we obtained time lapse between successive visits made by the boats for service at the dock. In cases involving propulsion system failure, this time lapse was taken as a measure of time to event occurrence. Given the nature and level of disaggregation of the data collected; it was possible to address the main research questions using event history data modelling technique.

Models to analyse time to occurrence of events are known variously as hazards models, duration models, Cox regression models, survival models, event history models and failure time models [

Mathematically,

If T denotes the response variable i.e. time before propulsion system failure, T ≥ 0 .

The survival function is:

S ( t ) = Pr ( T > t ) = 1 − F ( t ) (1)

The survival function in this case, gives the probability that a gearbox or propulsion shaft will survive past time t. As t ranges from 0 to 1, the survival function has the following properties:

It is non-increasing.

At time t = 0 , S ( t ) = 1 . In other words, the probability of surviving past time 0 is 1.

At time t = 1 , S ( t ) = S ( 1 ) = 0 . As time goes to infinity, the survival curve goes to 0.

In theory, the survival function is smooth. In practice, we observe events on a discrete time scale (days, weeks, months etc.). The hazard function h ( t ) , or rate is the instantaneous rate at which events occur, given no previous events.

h ( t ) = lim Δ t → 0 Pr ( t < T ≤ t + Δ t | T > t ) Δ t = f ( t ) s ( t ) (2)

The cumulative hazard describes the accumulated risk up to time t, H ( t ) = ∫ 0 t h ( u ) d u .

If we know any one of the functions S ( t ) , H ( t ) or h ( t ) , we can derive the other two functions.

h ( t ) = − ∂ log ( S ( t ) ) ∂ t (3)

H ( t ) = − log ( S ( t ) ) (4)

S ( t ) = exp ( − H ( t ) ) (5)

The Kaplan-Meier (KM) survival curve is defined as the probability of surviving in a given length of time while considering time in many small intervals [

Let t 1 < t 2 < ⋯ < t b denote the ordered event times in the sample. For t i , let d i denote the total number of failures occurring at time t i , s i denotes the total number that have not failed by time t i , n i denotes the total number at risk at time t i , and d i = n i − s i . Thus, Gokovali, Bahar & Kozak [

S ^ K M ( t ) = ∏ i : t i ≤ t ( 1 − d i n i ) = ∏ i : t i ≤ t ( s i n i ) (6)

and the Greenwood’s formula for standard error estimate of the KM estimator is given by:

S E ^ G { S ^ K M ( t ) } = S ^ K M ( t ) ∑ i : t t ≤ t d i n i s i (7)

The proportional hazards model otherwise known as Cox regression model according to Kaplan and Meier [

The hazard is modelled as:

h ( t / x ) = h o ( t ) exp ( β 1 x 1 + β 2 x 2 + ⋯ + β n x n ) (8)

where x 1 , ⋯ , x n are explanatory variables,

h 0 ( t ) : baseline hazard time t representing the hazard for a boat’s gearbox/shaft status with value 0 for all explanatory variables.

β 1 , ⋯ , β n : regression coefficients describing the impact of the covariates, which is estimated by the partial likelihood estimation procedure.

Parameter estimates in Cox model are obtained by maximizing the partial likelihood function for the observed data simultaneously with respect to h 0 ( t ) and β as proposed by Cox [

In

As shown in

Purpose of visit | Type of vessel | |||
---|---|---|---|---|

tug | supply | crew | Total | |

Shaft failure | 17 | 89 | 35 | 141 |

Gearbox failure | 7 | 52 | 14 | 73 |

Shaft/gearbox failure | 5 | 21 | 10 | 36 |

Maintenance | 5 | 32 | 12 | 49 |

Total | 34 | 194 | 71 | 299 |

Source: Author, field work.

Time (months) | |||
---|---|---|---|

Boat type | Status | No. of boats | Mean |

Tug | 0 | 5 | 5.347 |

1 | 29 | 8.326 | |

Supply | 0 | 32 | 5.126 |

1 | 162 | 5.229 | |

Crew | 0 | 12 | 4.798 |

1 | 59 | 5.205 |

Source: Authors, data analysis (based on dockyard records). 1: failed, 0: censored.

Other frequency distributions of data on factors affecting shaft and gearbox failure in service boats are listed in Appendix 3 and Appendix 4. These factors (which are dummy variables taking on values of 1 or 0) were used as explanatory variables in Cox regression analysis. The censor variable (see Appendix 1) is also a dummy with a value of 1 indicating shaft/gearbox failure and value 0 if censored.

In ^{th} month) in supply boats than in crew boats.

For tug boats, the probability of failure of propulsion components followed a similar pattern as in crew boats. As shown in ^{th} month point on the time axis. In other words, after 18^{th} month (in between repairs) survival probabilities drop to zero.

From the foregoing, it was observed that shaft and gearbox systems endurance showed a similar pattern in crew and tug boats. However,

Risk Factors | Hazard Ratio | Std. Err. | z | P > |z| |
---|---|---|---|---|

Insuff. Lub. Oil | 1.301 | 0.172 | 1.990 | 0.047 |

Impact | 1.619 | 0.223 | 3.500 | 0.000 |

Stress corrosion cracking | 2.328 | 0.405 | 4.860 | 0.000 |

Model fitting information | ||||

No. of Obs. = 299 | ||||

Log-likelihood = −1159.466 | ||||

LR Chi^{2}(3) = 44.09 | ||||

Prob > Chi^{2} = 0.0000 |

Source: Author, data analysis.

The significant risk factors affecting shaft and gearbox failures in service boats are according to coefficients of hazard ratio, stress corrosion cracking, impacts while underway at sea and insufficient lubrication oil in the gearbox or shaft bearings, see

In this study, we determined the frequency distribution of failures of shaft and gearbox components in supply, crew and tug boats. Specifically, it was found that each boat type exhibited particular frequency (time) and probability of failure. Shaft and gearboxes in Supply boats were found to have higher probability of failure than in crew boats and then followed by tug boats in this order. It was also found that probability of failure was higher within 0 - 10 month’s interval following boats’ visits to dockyard for repairs. The Cox regression outputs showed that failure in shaft and gearbox marine propulsion system could be attributed to the following factors: insufficient lubrication, impacts related to environmental condition of water or and stress corrosion cracking in propulsion system’s components. It is therefore proposed that these three factors could be controlled through proper design and strict adherence to maintenance schedule programme. The present research was based on a case study of a single dockyard. We assume here that a case study of this nature may limit generalizability of its findings. Thus, while we recognise this as a limitation, the methodology applied and findings are rather instructive and should provide a guide for expanded research on this theme in future studies involving multiple sampling units.

The authors declare no conflicts of interest regarding the publication of this paper.

Onwuegbuchunam, D.E., Ogwude, I.C., Igboanusi, C.C., Okeke, K.O. and Azian, N.N. (2020) Propulsion Shaft and Gearbox Failure in Marine Vessels: A Duration Model Analysis. Journal of Transportation Technologies, 10, 291-305. https://doi.org/10.4236/jtts.2020.104019

Key: 1: failed, 0: censored; Source: Authors; field work.

Key: 1: yes, 0: no; Source: Authors; field work.

Key: 1: yes, 0: no; Source: Authors; field work.

Key: 1: yes, 0: no; Source: Authors; field work.