A new approach to determination of the most critical multi-state components in multi-state systems is presented. The approach is based on solving an appropriate reliability optimization problem. The consideration is restricted on coherent and homogenous systems. Multi-state components may have different and distinct states which vary from complete failure to perfect functionality. The number of possible states is fixed and the same for all components and the system as a whole. The states correspond to different performance levels of components and the system. It is supposed that for each component state the corresponding probability and cost is known and that a higher state implies a higher cost. Further on, it is supposed that states of components are mutual statistically independent random variables. An original mathematical model for reliability calculation is developed and a corresponding optimization problem for identifying the most critical components is formulated and solved on numerical example.
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