Therefore the nth. maintainability Mn and the nth. increasing maintainability △ Mn are equal to the nth. Qn and △ Qn respectively.
Mn = 1 - R0n = 1 - (1 - Q0)n (3-5)
△ Mn = Mn- Mn-1 = R0n-1 - R0n ≧ 0 (3-6)
These two indices Mn and Δ Mn can be applied to evaluate the maintenance work as important evaluating indices for crew to take care of the nth. level redundant system.
It should be noticed that the highter level of redundant system would require the more man-power work on board isolated from land-relieves.
Among these evaluating indices there are some duality relationships between Rn and Mn, and between Δ Rn and Δ Mn due to above equations.
It is clear that the more levels of redundant system can obtain the higher reliability and the more safety due to Rn and Δ Rn because of their non-negative qualities and on the other hand it must require the harder maintainability for crew to take care of the more man-power work due to Mn and Δ Mn because of their non-negative qaulity too.
It is remarkable that the ratio of Δ Rn to Δ Mn is unity in the case of (R0=0.5=Q0) shown in Table 3-1A but its ratio is equal to unity or less than unity in the later of (R0=0.6, Q0=0.4) shown in Table 3-1B. This means that the advantage of redundant system can not always give the good conditions for crew on board where they have to manage any system of vessel without land relief in the case of redundant levels n ≧ 3.
4. MULTIVARIATE EVALUATION FOR MES WITH THREE INDICES
Dependability has both the two meanings of reliability and maintainability with suportability, therefore it would be very suitable (R3, R4, R5) to use the multivariate evaluation chart (MVC) like Fig.4-1 with three evaluating indices, which can be obtaind among them due to their dimensions too as follows;
MI [MH/1000Hr] = λ [occ./1000Hr] × mh [MH/occ.] (4-1)
In the JSRIC Data Base two kinds of evaluating indices of failure rate λ, average man-hour mh are stored as two important values, whose locations can be plotted inside a plae of horizotal axis and vertical one of logarithm scale in the MVC like Fig.4-1, therefore the third evaluating one of manning index MI can be seen as a declined straight line in the MVC. In the MVC the three evaluating indices λ mh and MI can be recognized at a glance.
Fig.4-1 shows two groups of evaluating indices whose simbols are ○, ○, □, □ added signs of Mi, Md, MT and Gi, Gd, GT for main propulsive power engines and generating ones respectively.
It is noticed that the white simbols for all the failures are located at the higher levels of failure rate λ (≧ 0.4 [occ./occ.], except G1) and the lower levels of average man-hour mh (≦ 9 [MH/occ.], except G4) than those of the black ones (○, □) for emergency ones at the higher level of mh (≧ 10 [MH/occ.], except Gd4) and the lower levels of failure rate λ (≦ 0.4 [occ./occ.], except Gd3) because they includes emergency failures shown in Fig.4-1.
With respect to some declined lines of manning index MI there can be seen several groups of evaluation indices (man-power per 1000Hr) which are more than 10, between 10 and 8, less than 5 and the lowest 0.5 [MH/1000Hr] . The first group are M2 and Gd3 (14.2, 13.8), the second one are M1 and G4 (8.84. 8.45), the third one are Md1 and Md2 (6.65, 6.96), the forth one are G1, G2, G3 and Gd2 (2.83, 2.59, 4.36, 3.50), and the last one are Gd1 and Gd4 (0.65, 0.51) respectively. The first group M2 and Gd3 would require lots of man-power works which are more than 122 man-hours per one year(8.760 [Hr]), and these two engine systems may be the worst systems among them, on the other hand the last group Gd1 and Gd4 may be 5.7 and 4.5 [MH/year] and the best ones even if the other two indices are loated at the long difference which means the different evaluating indices concerning with failure rate λ and average man-hour mh.
It shuold be noticed that the multi-variate evaluation chart MVC shown in Fig.4-1 has some properties and capabilities due to equation (4-1). If man-hour mh divided by m [men] number of maitenance crew, maintenance hour per each failure h [Hr/occ.], and then MI/m becomes to be total maintenance hour per 1000 [Hr].
