4. Optimal Preventive Replacement Age of Components of Main Engine Cooling System

　

4.1. Background

The main idea of this part is to find the correlation between the time/age in which equipment is maintained /replaced with the associated total cost. Since the preventive replacement does not guarantee/provide the most optimum cost, then the analysis must be done to determine the optimal preventive replacement age of the components, and verification must be delivered whether or not preventive replacement is necessary rather than operating the component until failure.

In the case of the main engine cooling system, where many components are connected in series, then the failure of one vital component would result in a system failure. The failure of the main engine cooling system would obviously have fatal consequences either to the engine itself or the ship operation in general. It is different to the other supporting systems of the main engine cooling system, for example, the fuel oil system, when the fuel oil system fail, then the engine would just cut out from the operating mode. On the other hand, when cooling system fails, then the most obvious consequence, overheating would induce considerable damage of the engine.

Briefly speaking, the main objectives of the following analysis is to find the performance balance between the amount spent on the preventive replacement with its resulting benefits, by determining the optimal preventive replacement age for the components to minimize the total expected cost of replacement per unit time.

　

4.2. Random Number Generator

Section 2 and 3 have described reliability analysis for component having constant failure rate. At these circumstances any preventive replacement would not give advantage to the system reliability, since such replacement will not reduce the probability of equipment failure occurring¹⁰⁾.

Consequently, a provision of failure records of the component during its wear out mode must be at hand. For simulation purposes, a random number generator is used to produce the failure records/data. More than 250 numbers of data are produced accordingly, with the objective to provide real randomness and uniform distribution, and providing the possibility of sequence repetition^9)*.

Weibull distribution was favored to represent the behavior of the failure in wear out modes. Some examples of the results are shown in Table 3. The reliability curve of the above 5 (five) different mode are shown in Figure 4

　

Table 3. Weibull Parameters

　

4.3. Optimal Preventive Replacement Age

The replacement model will be based essentially on the two conditions. Firstly, when the replacement time is not taken into account, and second, when replacement time is quite significant, and can not be ignored from the analysis.

For the first case, there are two cycles determine the failure mode of the model. The first cycle is when the component failure is due to a preventive replacement reason, and the second cycle is subject to failure replacement. Some notations will be employed to relate the total cost and reliability characteristic of the components. Those notations are:

　

Cp = the cost of preventive replacement

Cf = the cost of failure replacement

f(t)= the pdf of the failure times of the equipment

　

　

By the same concept as what has been described in the first case, the total expected replacement cost per unit time, when the failure and preventive replacement time are taken into account, is:

　

　

In the previous description, the determination of the failure distribution of each component of the main engine cooling system has been done by means of a computer program. Its failure distribution parameters, which reflect the failure characteristic of each component, have also been obtained. These parameters will then be gainfully employed to determine the reliability as well as the unreliability of each component as a function of operating time. The establishment of the expected length of failure cycle can then also be obtained by using those distribution parameters.

The determination of performance balance between the amount spent on the preventive replacement with its resulting benefits is thereupon evaluated by determining the optimal preventive replacement age for the components to minimize the total expected cost of replacement per unit time.

Some variations on the ratio between the cost of failure replacement (Cf) and the cost of preventive replacement (Cp) are also carried out with the main aim of finding the sliding trend of the optimum expected replacement cost.

　

Fig. 4 Reliability Curve for Different value of Beta

BACK　　　CONTENTS　　　NEXT