The Delphi method which is repeatedly used in collecting and analysing opinions of experts until a consensus is reached in resolving a decision problem [11] . Some of the merits of the Delphi technique are 1) participant experts can freely express their opinions since information is anonymously sourced creating no room for domineering experts to dictate the outcome which is usually the case of the conventional brainstorming technique [12] and 2) the process is cheap since through email, surface mail and sometimes face to face contact with individual participant experts, the researcher or investigator can obtain a consensus opinion from participating experts on an issue as compared to the traditional brainstorming technique where experts will need to convene in one place to reach a consensus.

The first step involves preparing a questionnaire and sending it to group of experts through means such as surface post and email. The responses are then obtained and processed. This is referred to the first round of the Delphi process. Based on the result of the first round a modified questionnaire is sent to the group of experts and again responses are obtained and analysed. This is the second round of the Delphi process. In most cases consensus are reached in the second round.

The TOPSIS method is a popular MCDM technique and was first proposed in 1981 by Yoon and Hwang [13] . The technique had been applied in the ranking of alternatives through distance measure. The optimum alternative is generally the one closest to the positive ideal solution. The methodological steps for TOPSIS analysis are as follows [14] [15] :

(1) Determination of the decision matrix: The decision matrix, X, can be represented as follows

where A_i represent alternative maintenance i,; B_j denotes decision criteria j, on the basis of which alternatives are judged. x_ij represent jth criteria with respect to ith alternative maintenance.

(2) Determination of normalised decision matrix

(3) Determination of the weighted normalised decision matrix

The weighted normalised decision matrix can be calculated by multiplying the normalised decision matrix by the weight of decision criteria and is expressed as:

where is the weight of the jth criterion. There are several technique available in the literature for the evaluation of criteria weights. The approach chosen in this paper is the AHP method because of its ability to utilised both qualitative and quantitative information in determining weights of decision criteria.

(4) Determination of the positive-ideal and negative-ideal solutions

The positive ideal solution and the negative ideal solution are evaluated respectively as follows:

where I is associated with the benefit criteria and is associated with cost criteria.

(5) Calculation of the separation measure

The separation of each alternative from the positive-ideal solution and from the negative-ideal solution, are evaluated, respectively as:

(6) Calculation of the relative closeness to the positive ideal solution.

The relative closeness of the alternatives to the positive ideal solution is evaluated as follows:

The alternative with the maximum value is the optimum solution.

However in many practical situations multiple experts or a group of experts are involved in the decision making process thereby bringing a great deal of complexity into the use of MCDM methods [16] . Different aggregation methods are available for combining experts’ preferences in group decision making. Either rank or score aggregation can be used. In this paper the score aggregation technique was chosen because rank aggregation may lead to rank reversal. In aggregating the scores of individual experts a simple arithmetic mean can be applied. The average of the individual experts TOPSIS scores for each maintenance alternative are referred to here as overall scores. On the basis of the overall score, maintenance strategy alternatives are ranked and the highest ranked chosen as the optimum solution.

Ten experts which comprises of 5 five academia and 5 from the shipping industry were selected. This was followed with the development of questionnaires based on 22 decision criteria obtained from literature. The questionnaires were then sent to the ten experts. Responses were then obtained and processed. Based on the result of the first round a modified questionnaire was sent to the ten experts and again responses were obtained and analysed. From the two round Delphi analysis of the 22 decision criteria, the number was reduced from 22 to 12. The twelve decision criteria are discussed as follows:

Spare parts inventories (C1). The amount of spare parts that should be available for each type of maintenance strategy.

Maintenance cost (C2). Cost of equipment, materials and labour for each maintenance strategy.

Crew training cost (C3). The cost that may be incur in training staff in order for them to have the required skills to use tools and techniques for performing maintenance task.

Equipment damage cost (C4). The cost consequences as a result of plant system equipment damage for each maintenance strategy.

Personnel safety (C5). Some equipment/components failure can cause serious injury or death of personnel on board ship. Maintenance strategy is generally chosen based on its ability to eliminate or reduce such failure.

Equipment safety (C6). In the event of failure of a particular component/equipment item, the question is how safe is the entire system. Greater attention is paid to parts that may result in severe damage to the system. A maintenance strategy that will reduce failure frequency to the lowest level is advisable.

Environment safety (C7). Failure of some parts of the marine machinery system can result in serious environmental hazards. The maintenance strategy is generally chosen based on its ability to eliminate or reduce such failures.

Minimisation of operational loss (C8). For each of the maintenance strategy there is an associated operational loss. Generally the preventative maintenance approach has greater capacity to minimise operational loss.

Equipment reliability (C9). Different maintenance strategy yield varying plant system reliability and the optimum solution is the one that will produce the highest reliability.

System failure characteristics (C10). The component failure characteristics; wear-in failure, random and wear-out failure are a key factor in selecting the most appropriate maintenance strategy for plant equipment. For example, Condition Based Maintenance (CBM) is suitable for components with random failure patterns, provided there is an identifiable warning sign for measuring the condition of the component.

Available monetary resource (C11). This is a vital factor in determining the optimum maintenance strategy. For example if available finance for maintaining the system cannot incorporate CBM, the plant manager is left with no choice other than to use alternative approach irrespective of the benefits of the CBM.

Equipment risk level (C12). Generally CBM strategy is preferred for very high risk equipment whose failure may result to irreversible damage to personnel, environment and plant system.

Having defined the decision criteria against which the maintenance strategies will be ranked, the next step is to apply the ranking tools, TOPSIS in evaluating the optimum maintenance strategy. A 5 point Likert scale was applied in this study in obtaining information from the three experts who are presented in Table 2. Since the case study uses three experts in determining the optimum solution, each of the expert’s information is used as input data into the TOPSIS methodology in turns to obtain their individual optimum solution.

In the application of TOPSIS to the sea water cooling pump of a marine diesel engine, the expert one information in the decision matrix in Table 2 was normalised using Equation (2) and the result is presented in Table 3. This is followed by the formation of the weighted normalised matrix using Equation (3) also shown in Table 3. Equations (4) and (5) were then applied to evaluate the positive ideal and negative ideal solutions respectively and results are presented in Table 4. Finally, Equations (6)-(8) were used to obtain the distance of each maintenance strategy alternative to the positive-ideal solution and to the negative-ideal solution together with relative closeness of each maintenance strategy to the ideal solution and the results of together with their rankings are shown in Table 5.

From Table 5, the best alternative is the OFCBM since it has the highest performance index of 0.9972 which is closest to the ideal solution. The ONCBM occupies the second position with a performance index of 0.8131 and the least preferred alternative is CM having the lowest performance index of 0.1357 and being in the last position.

The same TOPSIS methodology were followed in analysing expert 2 and 3 information and the results obtained are presented in Table 6 and Table 7 respectively.

The overall scores of maintenance strategy alternatives were evaluated by averaging the individual expert’s scores and the result is shown in Table 8. From the result, OFCBM occupies the first position having an overall score of 0.9542. Hence the optimum maintenance strategy is OFCBM. The second most preferred alternative is the ONCBM and the least preferred choice is CM with the lowest overall score of 0.1639. The CM approach being ranked in the last position is a clear indication that the marine industries is fast shifting from the reactive maintenance approach to Condition Based Maintenance methodology. Although OFCBM and ONCBM are both Condition Based Maintenance technique the preference for the OFCBM methodology may be as a result of the desire by most marine industries to minimise maintenance cost whilst maintaining optimum reliability of ship systems.

In validating the proposed methodology, the technique was compared with other approaches; AHP and PROMETHEE. From the comparative analysis, results show that the three techniques produce OFCBM as the best maintenance strategy for maintaining sea water cooling pump. Although AHP and PROMETTHE produces the same optimum solution with the TOPSIS methodology but the limitations of the AHP and PROMETHEE will make them unattractive to maintenance practitioners. The AHP as ranking tool will result to obtaining numerous pairwise comparison judgement which will make the evaluation process complicated. The PROMETHEE

technique has limitations such as evaluation process complexity and the need for maintenance practitioners or analysts to determine preference function for each of the decision criteria. On the other hand the TOPSIS technique evaluation process is quiet simple irrespective of the number of decision criteria used in evaluating alternative maintenance strategies and these characteristics will make it attractive to the maintenance practitioners.