Abstract
This research innovatively proposes a new two failure criteria sliding window system. In this system, there exist x linearly ordered multi-state elements and each element has different performance rates ranging from complete failure to perfect functioning. The system fails if either the total number of failed groups of r consecutive elements reaches k or the gap between any two adjacent failed groups of r consecutive elements is less than m working groups. To evaluate the reliability of the proposed system, we extend the universal moment generating function technique and suggest a corresponding algorithm. The reliability importance of the proposed system is also analyzed. Furthermore, we use the genetic algorithm to determine the optimal element allocation and demonstrate how the element allocation affects the system reliability. Both analytical and numerical examples are presented to illustrate the model and the algorithm.
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