This paper describes a total maintenance model which consists of the fewer full complement (M_s) on board with a propelling interval (T_s) and the more home port relief manpower (M_p) at land with a home port one (T_p) .
This model has to keep an allowable inventory of a limited length (L_c) of waiting lines corresponding to the accumulated maintenance man-hour (ΔMH) _s left untreated during T_s.
The following three queuing length modes are proposed whether the residual man-hour (ΔMH) _p of M_p during T_p is able to counterbalance (ΔMH) _s or not;
(A) absolute stable mode (a) ΔL_p > L_G-L_M
(B) temporary stable mode (b) : ΔL_p = L_G-L_M
(C) absolute unstable mode (c) : ΔL_p= L_G-L_N <L_G-L_M
where L_G; a length waiting lines of arrival at home port, L_G < L_C
L_M, L_N; ones of departure from home port <L_G
ΔL_p ; one corresponding to (ΔMH) _p
Utilization η_j and queuing length rate QLR l_j are defined as follows;
η_j= (⁴Σ_i=1T_jmh_i0/d⋅T_i0) / (M⋅D) _j=⁴Σ_i=1 (T_j/T_i⋅H_ij/D_j)
l_j=dL_j/dt=L_j/T_j=λ_j-μ_j=(ΔMI) _j/mh_j
where T_j; each interval of voyage, D_j; duty time of T_j, α; up ratio of reliability
T_i0, mh_i0; representative values of mean time between maintenance and mean man-hour per occurrence
λ_j, μ_j, H_ij; failure rate and maintenance rate and time of each interval T_j, and of each maintenance P_i
The temporary stable mode (b) requires the following conditions for each interval T_s, T_p, T_v (T_s +T_p = a period interval) ;
(1) necessary condition: η_s>1.0, L_c>L_G=L_s=l_s⋅T_s = (λ_s-μ_s) ⋅T_s>0
η_p<1.0, -L_c<L_p=l_p⋅T_p= (λ_p-μ_p) ⋅T_p<0
(2) sufficient one: η_v≤1.0, L_s+L_p = [(1-δ) ⋅l_s+δ⋅l_p] ⋅T_v<0
where δ; home port service interval rate = (T_p /T_v)
From the output informations of GPSS digital simulation for 8 hours maintenance model (MODEL II) which is able to give occurring rate λ, over time H_o and length of waiting lines L, some useful relationships among the above many variables.

View full abstract