PART V. Practices and Emerging Applications
4.6 Multi-state System Structure Optimization Problems
4.6.5 Other Problems of Multi-state System Optimization
In this section we present a short description of reliability optimization problems that can be
88 System Reliability and Optimization
Table 4.14. Parameters of the optimal solutions for system with different MPS elements
EA∗ EA C System structure
MPS RGS 1 RGS 2 RGS 3
0.950 0.951 27.790 3, 6,6, 6,6 1, 1, 1, 1, 1 1, 1,2, 3 1, 1 0.970 0.973 30.200 3, 6,6, 6,6, 6 1, 1, 1, 1 1, 1,2, 3 1, 1 0.990 0.992 33.690 3, 3,6, 6,6, 6 1, 1, 1, 1 1, 1,2, 3 4, 4 0.999 0.999 44.613 2, 2,3, 3,6, 6 1, 1, 1 1, 2,2 4, 4, 4
Table 4.15. Parameters of the optimal solutions for system with identical MPS elements
EA∗ EA C System structure
MPS RGS 1 RGS 2 RGS 3
0.950 0.951 34.752 4,4, 4,4, 4,4 1, 4, 4, 4, 4 2,2, 2 1, 3, 3, 3, 4 0.970 0.972 35.161 4,4, 4,4, 4,4 1, 1, 1, 4 2,2, 2,2 1, 3, 3, 3, 4 0.990 0.991 37.664 2,2, 2,2 4, 4 3,3, 3,3 4, 4, 4 0.999 0.999 47.248 2,2, 2,2, 2 3, 4 2,2 4, 4, 4, 4
solved using a combination of the UGF technique and GAs.
In practice, the designer often has to include additional elements in the existing system rather than to develop a new one from scratch. It may be necessary, for example, to modernize a system according to new demand levels or according to new reliability requirements. The problem of optimal single-stage MSS expansion to enhance its reliability and/or performance is an important extension of the structure optimization problem. In this case, one has to decide which elements should be added to the existing system and to which component they should be added.
Such a problem was considered by Levitin et al.[36].
During the MSS life time, the demand and reliability requirements can change. To provide a desired level of MSS performance, management should develop a multistage expansion plan.
For the problem of optimal multistage MSS expansion [41], it is important to answer not only the question of what must be included into the system, but also the question of when.
By optimizing the maintenance policy one can achieve the desired level of system reliability
(availability) requiring the minimal cost. The UGF technique allows the entire MSS reliability to be obtained as a function of the reliabilities of its elements. Therefore, by having estimations of the influence of different maintenance actions on the elements’ reliability, one can evaluate their influence on the entire complex MSS containing elements with different performance rates and reliabilities. An optimal policy of maintenance can be developed that would answer the questions about which elements should be the focus of maintenance activity and what should the intensity of this activity be [42, 43].
Since the maintenance activity serves the same role in MSS reliability enhancement as does in- corporation of redundancy, the question arises as to what is more effective. In other words, should the designer prefer a structure with more redun- dant elements and less investment in maintenance or vice versa? The optimal compromise should minimize the MSS cost while providing its desired reliability. The joint maintenance and redundancy optimization problem [37] is to find this opti- mal compromise taking into account differences in reliability and performance rates of elements composing the MSS.
Multi-state System Reliability Analysis and Optimization 89 Finally, the most general optimization prob-
lem is optimal multistage modernization of an MSS subject to reliability and performance re- quirements [44]. In order to solve this problem, one should develop a minimal-cost modernization plan that includes maintenance, modernization of elements, and system expansion actions. The ob- jective is to provide the desired reliability level while meeting the increasing demand during the lifetime of the MSS.
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Combinatorial Reliability Optimization
Chapt e r 5
C. S. Sung, Y. K. Cho and S. H. Song