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In the reliability literature, reliability allocation is an important and widely studied topic. The existing reliability allocation methods, however, have limitations, including imprecise system decomposition, single-factor consideration, and poor practicability. To overcome those limitations, we propose an integrated fuzzy reliability allocation method based on micro-motion decomposition, cost function, and multi-factor analysis. The problems in the existing methods caused by equally weighted factors and influences of failures were overcome by correcting the traditional risk priority number method and evaluating the uncertainties and subjective factors during allocation using fuzzy language and triangular fuzzy number. A cost model was established based on the state of the art, subsystem intricacy, and environmental conditions, with which the issues of difficulty applying cost statistics and computational complexity in the current allocation methods were solved. The contribution of this paper is as follows. A fast approach of Pareto-optimal solution recommendation using the Pareto reliability index has been utilized to recommend a list of optimal ranking for decision-makers. Besides, the moving mean of the average precision and the moving mean standard deviation are utilized to demonstrate the trend of the evolutionary process. A multi-objective swarm bat algorithm has been developed to handle the multi-objective problems and its feasibility has been verified in a case study comparing the performance of the proposed method with that of the existing methods.

Optimal Micro-Motion Unit Decomposition-Based Reliability Allocation for Computer Numerical Control Machine Using the Swarm Bat Algorithm