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Machining accuracy retainability is considered to be one of the most important aspects in the process of performance evaluation and optimization design of the machine tools. Reliability based design optimization (RBDO) and robust design optimization (RDO) are the tools that search for safe structural systems with minimal variability of response when subjected to uncertainties in design parameters. The aim of this paper is to propose an approach that simultaneously considers reliability and robustness to allocate geometric accuracy of components for improving machining accuracy retainability under certain design requirements. Based on homogenous transformation matrices (HTMs), a comprehensive volumetric model explaining how individual errors in the components of a machine affect its volumetric accuracy (the coupling relationship) was established. By applying high-order moment standardization technique (HOMST), reliability and sensitivity with single failure mode were obtained and then the reliability model and the sensitivity model with multiple failure modes were developed and common methods such as Narrow bounds, AFOSM and Monte Carlo were used for verification and comparison. Meanwhile, a cost model taking manufacturing cost and present worth of expected quality loss into consideration was introduced. By taking the minimum possibility of failure and cost of machine tools as criterions and taking the reliability of machine tools as constraint of optimizing the basic parameters of machine tools, an approach to optimize the machining accuracy retainability of multi-axis NC machine tool based on robust design was developed and an example of improving the machining accuracy retainability for a five-axis NC machine tool was used to demonstrate the effectiveness of this approach. This study implies that it is possible to obtain the relationships between geometric errors and specify the accuracy grades of main feeding components of mechanical assemblies. [ABSTRACT FROM AUTHOR]