3. REDUNDANT MODEL OF MES (Marine Engine system)

　

3.1 REDUNDANT MODEL OF MES

If a ship had has fifteen cylinders shown in Fig.3-1A, there could be supposed two kinds of combinaiton which are a) 3 sets with 5 cylinders and b) 5 sets with 3 cylinders. Both of them have same out-put power, the later one b) has the more level of redundant engine sets than that of the fomer. The fact that the more redundant system has the higher reliability and the more safety can be demonstrated by the combination diagram shown in Fig.3-1B, can prove a parallel redundant sets (R_n, Q_n) with n=2 degree of redundant level, in which there are three kinds zones. They are white area (R₀. × R₀), two single dotted lines ones (R₀. × Q₀) and double dotted lines ones (Q₀ × Q₀).

　

Fig. 3-1A Two kinds of redundant engine systems of same output-power with 15 cylinders

Fig 3-1B Combination diagram of parallel redundant system with original reliability R₀=0.6 and un-reliability Q₀=0.4 n=2

　

The two areas of single {dotted lines R₀ × Q₀, Q_O. × R₀ (=0.24)} are very important for the model of redundant system to increase the highter reliability R₂ (=0.84) and to decrease the worse un-reliability Q₂ (=0.16) than those of original reliability R₀ (=0.6) and un-reliability Q₀. (=0.4).

In general case of nth. level of redundant system the following equations can be obtained to give nth. reliability R_n and nth. un-reliability Q_n from the original reliability R₀ and un-reliability Q₀ which is equal to n=1 redundant level system (R₁, Q₁).

　

R_n = 1 - Q_n = 1 - (1 - R₀)ⁿ　(3-1)

Q_n = 1 - R_n = 1 - (1 - Q₀)ⁿ　(3-2)

where 1.0 ≧ R₀, Q₀ ≧ 0

　

And then the set of increasing reliabiltiy and the decreasing un-reliabilty (△R_n, △Q_n) can be obtained by the following equations from nth. reliability and un-reliability (R_n, Q_n) and the n-₁th. reliability and un-reliability (Rn-1, Qn-1)

　

△R_n = R_n - R_n-1 = Q₀^n-1 - Q₀ⁿ ≧ 0 (3-3)

△Q_n = Q_n - Q_n-1 = R₀^n-1 - R₀ⁿ ≧ 0 (3-4)

　

3.2 THE MAINTAINABILITY M n AS EVALUATION INDICES FOR MAINTENANCE WORK

On board those who have to take care of all the machineries belonged to marine engine system (MES) have to maintain and repair anything wrong which belongs to all the areas dotted lines sone shown in Fig.3-1B. In the other words they could be free from maintenance work as far as MES would be at the normal state (R₀, R₀) shown in Fig.3-1B.

　

Table 3-1A Caluculated values of nth. Redundant model Rn, ΔRn, Qn, Mn and △Mn

Table 3-1B Caluculated Values of nth. redundant model Rn, Qn, Mn and △Mn

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