Optimal structure of multi-state systems with multi-fault coverage

Due to imperfect fault coverage, the reliability of redundant systems cannot be enhanced unlimitedly with the increase of redundancy. Thus it is essential to study the optimal structure of redundant systems. This paper considers a multi-state series-parallel system with two types of parallelization: redundancy and work sharing. Different from existing works which consider single-fault coverage, multi-fault coverage is considered in order to adapt to a wider range of fault tolerant mechanisms. For multi-fault coverage, the coverage factor of an element failure in a work sharing group depends on the status of other elements. It is assumed that the uncovered failures in the elements belonging to the group of elements sharing the same task can cause failure of the entire group. The optimal trade-off between the two kinds of parallelization has been studied based on various settings of fault coverage factor. Examples of data transmission systems and task processing systems are presented to illustrate the applications of results.