1 Introduction

Maintenance is the essential part of production process in today’s industry. The primary goal of maintenance is to avoid or mitigate consequences of failure of equipment. There are different types of maintenance strategies applied in industry such as corrective maintenance, preventive maintenance, predictive maintenance etc. These techniques have been evolved over a period of time and are grouped under various generations (Moubray 1997) (Arunraj and Maiti 2007). The 1st generation (1940–1955) is based on breakdown maintenance, the 2nd generation (1955–1975) is based on time based maintenance and the 3rd generation (1975–2000) is based on condition based maintenance. The current generation (yr 2000 +) is called 4th generation and here the prime focus will be on elimination of failures. Each one has its own advantages and disadvantages. Challenge here is to choose the proper ones for the specific operation conditions and equipment.

Reliability Centred Maintenance (RCM) is a process to ensure that systems continue to perform their intended function in the present operating environment and is attributed as third generation technique. Successful implementation of RCM will lead to increase in cost effectiveness, reliability, machine uptime, and a greater understanding of the level of risk that the organization is managing. RCM is widely being used in airline industry (MIL-STD-2173 (AS) 1986; Ahmadi et al. 2009; Guo et al. 2016), nuclear industry (Durga et al. 2007; Kadak and Matsuo 2007), transportation (Carretero et al. 2003), defense sectors (MoD 2006), medical industries (Shamayleh et al. 2020; Mahfoud et al. 2018, 2016), railway sector (Singh et al. 2020) etc. Bae et al. (2009) applied RCM technique to a standard electric motor unit subsystem and optimized the maintenance time using evolutionary algorithm. Ilya and Tore (2012) have worked on a methodology for development of condition based maintenance program for surface drilling machine. Seyed and Uday (2016) applied RCM technique to fully automated underground mining machineries. Lazakis et al. (2009) utilized a methodology combining risk and criticality approach to develop effective maintenance strategies for a ship.

Grall et al. (2001) applied condition-based maintenance policy for stochastically deterioration systems. Hiroyasu (2003) utilized Genetic Algorithms for optimization of diesel engine emissions and fuel efficiency. Abdul-Kader (2009) designed a prototype fuzzy knowledge base system to improve the capabilities of fault tracing for a ship diesel engine. Girtler Jerzy (2015) presented semi-Markov models of technical state transitions for diesel engines, useful for determining the reliability of engines. Awang et al. (2020) presented a study of 2-stroke main propulsion marine diesel engine characteristic using ultrasound signal monitoring condition based maintenance. Shi et al. (2023) proposed an integrated decision-making approach that uses the 2-tuple linguistic term to prioritize key practices for marine diesel engine maintenance.

Based on the literature review the following gap areas have been identified such as, RCM is being applied in various industries however it is very less explored and utilized in marine operations. Failure rate models for components under specified environmental conditions are not available. Traditionally, system reliability has been analyzed as a binary perspective, assuming the system and its components exist in two states that is either completely functioning or failed state. However, performance of some of the components varies with time and one needs to capture this behavior precisely to represent the component reliability correctly. Hence, in this manuscript reliability modeling of performance degradation of the components is dealt with Markov models and the required data is evaluated from condition monitoring techniques. The marine diesel engine considered for the study mainly maintained by the Planned Preventive Maintenance schemes and is not cost effective due to the lack of optimal maintenance strategies. Hence, the primary objective of the current study is development of new maintenance schemes by using RCM technique for conventional marine diesel engine.

To achieve the above mentioned objectives the work was divided into two parts, in the first part reliability of the marine diesel engine was analysed by carrying out Failure Modes and Effects Analysis (FMEA) (Banks et al. 2001; Peters et al. 2018; Muzakkir et al. 2015) to identify various failure modes of the components and performed Fault Trees Analysis (FTA) (Peters et al. 2018). Markov analysis has been used for modelling performance degraded components and utilised in FTA. Post completing the FTA, based on the importance ranking, critical components have been obtained for optimizing the maintenance schedules. In this paper genetic algorithm approach has been used to optimize the maintenance schedules.

2 Reliability centered maintenance

The different maintenance strategies developed over the decades as discussed previously are briefly explained as follows:

  1. a)

    Breakdown Maintenance (First Generation): This maintenance strategy is also known as corrective maintenance. This strategy focuses on corrective actions which are mainly on the objective “NO FIX UNLESS BROKE” (Moubray 1997). This strategy has no downtime of assets between failures. But this has few disadvantages as well. This strategy requires large spare part inventories. It leads to unscheduled work outages and longer restoration time with high cost. This strategy ultimately leads to collateral damage with low manageability of budget and safety of personnel.

  2. b)

    Time based maintenance (Second Generation): This maintenance strategy is based on fixed cycle repair. It focuses on reducing risk of catastrophic failure, prevents equipment failure and overcomes disadvantages of Run-to-Failure strategy. This strategy has reduced operation time per cycle. Also, it doesn’t give any importance to condition-based maintenance. Sometimes this strategy cannot be implemented due to operational restrictions.

  3. c)

    Condition Based Maintenance (Third Generation): This maintenance strategy provides a continuous risk assessment. It integrates with total resource planning. The focus is on higher plant availability and reliability, greater safety, better product quality etc. It accounts for all the disadvantages of Run-to-Failure and Fixed Frequency maintenance. But this strategy leads to higher implementation and operating costs for labour and condition monitoring system.

Whereas, RCM over comes the disadvantages of other maintenance techniques in which the maintenance strategies are optimized based on the reliability information and conditioning of the components. RCM is attributed as third generation technique, but it is being widely used by various industries. John Moubray (1997) in his publications clearly brought out the need of RCM over other maintenance strategies and also mentioned various requirement, methods and procedures to carry out RCM on any machinery. The basic steps involved in RCM (Moubray 1997) (Seyed and Uday 2016) are shown in Fig. 1.

Fig. 1
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Basic steps of RCM (Moubray 1997; Seyed and Uday 2016)

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3 Case study on marine diesel engine

Engines in which combustion takes place inside the cylinder are called internal combustion engines (Pulkrabek 2003). They are classified into spark ignition engines and compression ignition engines. Petrol engine is an example of spark ignition engine whereas diesel engine is an example of compression ignition engine. In diesel engine kinetic energy is obtained from the combustion of diesel fuel. In marine industryl diesel engines are being used for different purposes. In this paper an onboard diesel engine which is used for power generation (also called diesel generators) has been considered.

Based on the procedure explained previously, RCM was implemented on the marine diesel engine. The basic steps followed in the procedure are FMEA for identification of various failure modes of the components, FTA for estimating the system reliability and thereby identified the critical components for the optimization problem. In the FTA, for estimating the system reliability one needs to input the failure data of the components. This failure data for the components was obtained either from operating experience or from generic data sources. However, the failure probability of performance degraded components such as journal bearing was obtained by conducting Markov analysis for which input was taken from condition monitoring techniques such as equipment vibration signals. The above steps are explained in detail in the subsequent sections and also shown in Fig. 2.

Fig. 2
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Implementation of RCM for marine diesel engine

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3.1 System description

Diesel engine fitted onboard has several components and these components are mainly divided into 5 systems such as starting air system, lube oil system, fuel system, cooling water system and main components. Starting air system deals with the service air and control air used for starting the diesel engine (Fig. 3) (Ankush 2019). As the diesel engine considered here is of heavy duty, the engine starts requires service and control air. Lube oil system (Fig. 4) (Ankush 2019) is the lifeline of the diesel engine and is required to lubricate all the moving parts/components of the diesel engine. Fuel system is responsible for the combustion inside the diesel engine. Apart from fuel (i.e. diesel), this system consists of components which provide ideal condition for fuel to ignite inside the engine. Cooling water system is required to take out the used heat from the engine to the sink (i.e. sea). In this system fresh water with some additive is being used and allowed to flow through various components of the diesel engine. Main components, though it is not the system but all the internal components which are the heart of the engine are categorized under this heading. The important main components of the diesel engine which are considered for the analysis are crankshaft, camshaft, piston, connecting rod, gear train, cylinder head assembly, cylinder liner, getefo coupling etc.

Fig. 3
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Schematic of starting air system (Ankush 2019)

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Fig. 4
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Schematic of lube oil system (Ankush 2019)

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3.2 FMEA of marine diesel engine

FMEA has been carried out for various sub systems of diesel engine (Banks et al. 2001) (Muzakkir et al. 2015) (Yan et al. 2011).During FMEA, each component was further identified with their sub component and their failure modes were identified. An FMEA sheet developed for main components of diesel engine is shown in Table 1.Post completion of FMEA, it becomes evident that how each component contributed to entire system failure. But to exactly know the importance of each component FTA has been carried out which provided the list of critical components leading to entire system failure.

Table 1 FMEA sheet for main components of marine diesel engine
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3.3 FTA of marine diesel engine

From the system description it is clear that the entire diesel engine can be divided into 5 important systems. From the FMEA various failure modes of each component/sub component were identified and this information was used in FTA. Fault trees developed for the marine diesel engine are shown in the Figs. 5 and 6. It can be seen that diesel engine failure will occur if any of the 5 systems fail. The fault tree for each system is further developed to represent the system failure as combination of sub component failures. Each sub component failure is represented with corresponding failure mode as identified in FMEA. The inputs for FTA in terms of failure rates and failure probabilities for the components were obtained from operating as well as generic data sources. However, for the performance degraded components separate reliability modeling has been carried out as explained in the following section. Post analysis, importance ranking of the components was obtained according to the importance of the components.

Fig. 5
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Fault tree of marine diesel engine

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Fig. 6
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Fault tree of marine diesel engine starting air system

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4 Reliability modeling of performance degraded components

Traditionally, system reliability has been analyzed as a binary perspective, assuming the system and its components can exist in two different states that are either completely functioning or failed. However, performance of some of the components varies with time and one needs to capture this behavior precisely to represent the component reliability correctly. Hence, in this study, reliability modeling of performance degraded components has been dealt with Markov models (Sharabah et al. 2006; Feng 2013; Kumar and Jackson 2008; Dong et al. 2014) and the required data is evaluated from condition monitoring techniques. In the present study this is demonstrated with a case study on journal bearing of the marine diesel engine.

There are several types of bearing which are used in the diesel engine. But the most important bearing which especially leads to the catastrophic failure of the diesel engine is the Journal Bearing. It is used in the diesel engine to provide support to the crankshaft. Journal bearing is also used for taking axial and radial loads generated from rotation of crankshaft and firing in cylinder respectively. There are six such bearings on the type of engine considered.

4.1 Failure mechanisms

Before we analyze and model the performance degradation of Journal bearing it is necessary to understand the various failure mechanisms of it. Consider the hydrodynamic sliding journal bearing, some of the important failure mechanisms are scoring due to foreign matter or dirt, faulty assembly, misalignment, shaft instability due to oil whirl etc. For more details of the failure mechanisms one can refer (Muzakkir et al. 2015) (Yan et al. 2011).The above-mentioned failure mechanisms were difficult to detect and hence, in this study condition monitoring techniques such as vibration analysis (BoWu and Ming-quanQiu 2017) (Duarte José Caldeira 2007) has been utilized to detect them.

4.2 Analyzing vibration signals

In order to model the right degradation model, it was necessary to understand the vibration signal obtained from the new bearing and the degraded bearing. Thus, raw vibration data for a journal bearing was extracted from the field. This raw data gives shock acceleration in time domain. In order to differentiate the vibration data of faulty bearing and new bearing, data overlapping was done and same is presented in the Fig. 7.

Fig. 7
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Comparison of new journal bearing vibrations with the defective bearing

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It is obvious from Fig. 7 that there is a deviation in the signal however it is very difficult to predict the degree of degradation and failure mechanism. One can use the concept of Root Mean Square (RMS) value to detect the degradation of the component (BoWu and Ming-quanQiu 2017) (Duarte José Caldeira 2007). This can be found out from the vibration signal collected over a period of time. Figure 8 shows the variation of velocity RMS value with respect to time. From the trend line one can see the degrading performance of the journal bearing. In order to find out the failure mechanism from the vibration signal the following procedure has been adopted.

  1. a)

    Obtain the vibration signal in time domain of defect free and defective component

  2. b)

    Convert the time domain signal in to frequency domain by using Fourier transformation method

  3. c)

    Compare the peaks obtained in frequency domain of both the signals

  4. d)

    Wherever there is mismatch in the amplitude of a particular frequency, one can conclude that the component is degraded due to the failure mechanism corresponding to that frequency.

Fig. 8
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Velocity RMS vs running hours

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The above procedure was applied to the journal bearing and the failure mechanism was identified. Based on the signals obtained in the frequency domain the prominent peak was found at 0.4X order. The same can be seen in the Fig. 8a, b and c. As explained earlier, the peak observed was because of the defect in Journal bearing due to Oil whirl.

4.3 Markov analysis

Based on the nature of parameters either discrete or continuous, Markov processes can be classified considering the state space and time domain of the process. In this way Markov processes can have four classifications based on time and state spaces, while each of them could be discrete or continuous. A Markov process whose state space is discrete is designated as a Markov-chain. In the present study, to address the deterioration of the system, discrete state space and continuous time domain model has been considered and hence, we have used the concepts of continuous time Markov chains.

In order to model the performance degradation of journal bearing from reliability point of view it is necessary to classify the various degradation phases in terms of transition states. As shown in Fig. 8, as per the RMS value of the vibration signal, the journal bearing can exist in following 4 states.

  1. a)

    Green (New Bearing with minimum vibration readings, RMS < 5 mm/s)

  2. b)

    Green 1(Old bearing but still in good working condition, 5 mm/s < RMS < 7 mm/s)

  3. c)

    Yellow (Old bearing having identifiable defect, 7 mm/s < RMS < 14 mm/s)

  4. d)

    Red (Old Bearing, time for replacement, RMS > 14 mm/s)

Based on the above mentioned transition states, various transition rates are calculated based on the vibration signals obtained over a period of time and are tabulated in Table 2.

Table 2 Various transition rates in Markov model
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After defining the states and transition rates for Markov analysis, one can represent them in state space diagram as shown in Fig. 9.In this model apart from the sequential effect, transition due to loss of lubrication (from state 1 to 3) and misalignment (state 0 to 2) were considered. The solution for the Markov model can be obtained by solving the Differential Equations (DEs) mentioned as below. These DEs have been solved using Euler’s forward differential scheme and estimated the unavailability of the bearing as a function of time and the same is shown in Fig. 10.

$$\frac{{\mathrm{dP}}_{0}}{\mathrm{dt}}= -{\mathrm{P}}_{0}(\mathrm{t})({\uplambda }_{1}+{\uplambda }_{5})$$
(1)
$$\frac{{\mathrm{dP}}_{1}}{\mathrm{dt}}= {\mathrm{P}}_{0}\left(\mathrm{t}\right){\uplambda }_{1}- {\mathrm{P}}_{1}(\mathrm{t})({\uplambda }_{2}+{\uplambda }_{4})+{\mathrm{P}}_{2}(\mathrm{t})\upmu$$
(2)
$$\frac{{\mathrm{dP}}_{2}}{\mathrm{dt}}= {\mathrm{P}}_{1}\left(\mathrm{t}\right){\uplambda }_{2}-{\mathrm{P}}_{2}\left(\mathrm{t}\right){(\uplambda }_{3}+\upmu )+{\mathrm{P}}_{0}\left(\mathrm{t}\right){\uplambda }_{5}$$
(3)
$$\frac{{\mathrm{dP}}_{3}}{\mathrm{dt}}= {\mathrm{P}}_{2}\left(\mathrm{t}\right){\uplambda }_{3}+{\mathrm{P}}_{1}\left(\mathrm{t}\right){\uplambda }_{4}$$
(4)

where Pi(t), i = 0, 1, 2 is the probability being in state 0, 1, 2.

Fig. 9
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Variable failure rate model with repairs and sudden loading

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Fig. 10
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Unavailability of journal bearing

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5 Optimization of maintenance schemes

Based on the fault tree analysis critical components of diesel engine were identified and these components were considered for maintenance optimization. In order to conduct the optimization, availability and cost model of the diesel engine are required which are discussed in the following sections.

5.1 Availability and cost model

The critical components considered in the present analysis are Journal Bearing, Crank Shaft, Sea Water Pump, Valve guide and Centrifugal Filter. System availability depends on the above mentioned components availabilities. As the system failure takes place if any one of the components fail this system can be considered as series system. Using these critical components, availability model of the marine diesel engine can be written as follows:

$${A}_{Sys}={\prod }_{k=1}^{5}{A}_{k}$$
(5)

Now availability of each component can be represented with following Eq. (6) which is based on the age replacement model (Bae et al. 2009; Antonella et al. 2012; Kumar and Westberg 1997; Zhang et al. 2012; Zhao et al. 2017). As per this model, downtime of the component has two parts, in the first part if the component fails at any point of time before the PM interval (T), it gets repaired with mean time to repair as βF and comes back to the normal operation immediately. In the second part, the component gets replaced at every PM interval T with mean time to replace as βT.

$$A(T)=\frac{{\int }_{0}^{\mathrm{T}}\mathrm{R}\left(\mathrm{t}\right)\mathrm{dt}}{{\int }_{0}^{\mathrm{T}}\mathrm{R}\left(\mathrm{t}\right)\mathrm{dt}\mathrm{+}{\beta }_{F}\mathrm{F(t) + }{\beta }_{T}\mathrm{R}(\mathrm{t})}$$
(6)

On the other side, cost model is necessary to estimate the cost involved in both preventive maintenance and corrective maintenance. The basis of this cost model was obtained from age replacement model (Bae et al. 2009; Antonella et al. 2012; Kumar and Westberg 1997; Zhang et al. 2012; Zhao et al. 2017). Corrective maintenance being the costly process due to replacement of components, should be avoided by obtaining the optimum time periods of preventive maintenance. In order to get the optimum period firstly the cost model needs to be defined for which cost per unit time, C(T) can be defined as the ratio of the expected cycle cost (ECC) and the expected cycle length (ECL)

$${C}_{S}=\frac{\mathrm{Total \ expected \ cost \ per \ cycle}(\mathrm{E}[\mathrm{C}])}{\mathrm{Expected \ cycle \ length}(\mathrm{E}[\mathrm{T}])}$$
(7)

where ECL is given by

$$E\left(T\right)={\int }_{0}^{\mathrm{T}}R\left(t\right)dt$$
(8)

Let Cf and Cp denote the average cost of a CM and PM replacement, respectively. As a result, E[C] is given by

$$E\left[C\right]={\mathrm{C}}_{\mathrm{F}}\mathrm{F}\left(\mathrm{t}\right)+{\mathrm{C}}_{\mathrm{p}}\mathrm{R}\left(\mathrm{t}\right)$$
(9)

Therefore,

$$C(T)=\frac{{C}_{F}\mathrm{F(t) + C}{\mathrm{p}}\mathrm{R}(\mathrm{t})}{{\int }_{0}^{\mathrm{T}}\mathrm{R}\left(\mathrm{t}\right)\mathrm{dt}}$$
(10)

One can also represent availability and cost models in terms of component hazard rate and repair rate. For the case of constant hazard rate (exponential distributed failure times with constant failure rate λf) the reliability model can be given as:

$$R\left(T\right)={e}^{-{\lambda }_{f}t}$$
(11)

Similarly, for the case of increasing hazard rate model considering the two parameter Weibull distribution with α as scale parameter and β as shape parameter, the reliability model can be represented as:

$$R\left(T\right)={e}^{-{\left(\frac{t}{\alpha }\right)}^{\beta }}$$
(12)

5.2 Genetic algorithms

Once the basic models of availability and cost are obtained, one can perform the optimization analysis. The objective function and constrains are defined as follows:

Minimize Cost

$${\text{C}}_{\mathrm{s}}=\sum_{k=1}^{5}\frac{{C}_{Fk}{F}_{k}\mathrm{(t)} + {C}_{\mathrm{pk}}{R}_{k}\mathrm{(t)}}{{\int }_{0}^{\mathrm{T}}{R}_{k}\mathrm{(t)}\mathrm{dt}}$$
(13)

Maximize Availability

$${A}_{Sys}={\prod }_{k=1}^{5}\frac{{\int }_{0}^{\mathrm{T}}{R}_{k}\mathrm{(t)}\mathrm{dt}}{{\int }_{0}^{\mathrm{T}}{R}_{k}\mathrm{(t)}\mathrm{dt}\mathrm{+}{\beta }_{Fk}F\mathrm{(t) + }{\beta }_{Tk}{R}_{k}\mathrm{(t)}}$$
(14)

Subject to

$${\prod }_{i=1}^{5}{A}_{i}>{A}_{sys, present}$$
(15)
$${A}_{i} < 1, 2, .., 5 $$
(16)

Since it is a multi objective optimisation problem, in the present study Genetic Algorithms (GAs) has been utilized to optimize the maintenance schemes due to its fast convergence and good efficiency.

GAs are search algorithms that are developed on the basis of genetics and natural selection. They are normally used in the fields of search and optimization problems to get quality solutions. In these algorithms natural selection process is simulated, that means, those species which are able to survive and reproduce will go to the next generation by adapting themselves to the environment changes in the current generation. In other words, in these problems survival of the fittest is being simulated. Each generation consist of a population of individuals and each individual represents a point in search space and possible solution. The terms like gene, chromosome and population are typically used in these algorithms which are pictorially represented in Fig. 11 (Goldberg 1989; Haupt and Haupt 2003; Deb 2011).

Fig. 11
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Description of gene, chromosome and population

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There are various steps in the algorithm, these are briefly explained as follows. Initially a population of certain size is randomly chosen and a fitness score is assigned to each individual of the population which shows the ability of an individual to compete. The individuals with better fitness scores are selected who can mate and produce better offspring by combining chromosomes of parents. In each simulation the population size is kept static and hence, provision has to be created for newly arrived individuals. This is done by making some individuals to die and they are replaced with new arrivals. In this way new generation is created and only the fittest one will survive over the successive generations and better solutions will arrive. The population is converged, once the off springs produced in the current generation do not have significant difference with that of previous population. Figure 12 shows the flow chart of GA algorithm. In the present GA algorithm roulette wheel selection method, bit string mutation and two point crossover method have been utilized.

Fig. 12
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Flow chart of GA algorithm

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6 Results and discussions

Based on the procedure explained in the previous section optimization of maintenance schemes has been carried out. The various input parameters used as part of GAs is listed in Table 3.The old maintenance routine is shown in Fig. 13. The availability and cost models for various components have been shown in Figs. 14, 15, 16, 17 and 18. From the Fig. 14, it can be seen that for the case of journal bearing the optimum value of availability is existing at 2600Hrs of PM interval, whereas the current PM interval is 1500Hrs. Considering the cost model, the optimum value of cost exist at 2400Hrs of PM interval. Similarly, from the Fig. 16 it can be seen that for the case of valve guide the optimum value of availability exist at 675Hrs of PM interval, whereas the current PM interval is 300Hrs. However, the optimum value of cost exists at 600Hrs of PM interval. The similar condition exists for all other components. As the optimum values of availability models and cost models do not exist at the same PM intervals it is required to identify the optimum values of PM interval which maximizes availability and minimizes cost which is a multi objective optimization problem. In the present study GAs have been utilized to optimize the parameters.

Table 3 Input parameters used in GAs
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Fig. 13
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Old maintenance routine pre optimization

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Fig. 14
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Availability & cost Vs PM interval for bearing

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Fig. 15
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Availability & cost Vs PM interval for crank shaft

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Fig. 16
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Availability & cost Vs PM interval for valve guide

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Fig. 17
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Availability & cost Vs PM interval for sea water pump

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Fig. 18
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Availability & cost Vs PM interval for centrifugal filter

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The optimized maintenance schemes obtained using GAs is shown in Fig. 19. When the results were compared it was found that optimization increased the availability of the system from 0.917 to 0.958. Also the cost per unit time has been reduced from 188.46 to 135.65. It means because of optimization the net gain of system availability is 4.5% with saving of 28% in cost. The Mean Time between Failures (MTBF) of components like bearing, crankshaft and sea water pump is above the new proposed maintenance schedule. Thus, the results can be implemented to upgrade the present maintenance schedule. The new optimized schedule is the result from the operating experience and historic data of marine diesel engine fitted on board single platform. The availability and cost optimization results are shown in Table 4.

Fig. 19
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New maintenance routine post optimization

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Table 4 Availability and cost optimization results
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7 Conclusions

In this paper Reliability Centered Maintenance (RCM) has been implemented on the marine diesel engine. Initially FMEA has been carried out and based on the FTA analysis critical component have been selected for optimization. Reliability modeling of performance degraded components (journal bearing) has been dealt with Markov analysis and the data required for the same is obtained by analyzing the vibration signals obtained from the field. Genetic Algorithms has been used as optimization technique for optimizing the maintenance schemes of critical components of diesel engine. After the optimization system availability was improved by 4.5% with cost saving of 28% per unit time. Also, these results were analyzed and new preventive maintenance time period was proposed.