Applying FAHP to safety and risk assessment of CNC spindle system based on Hilbert space

Referring to the high-speed motorized spindle of a computer numerical control (CNC) machine tool, the safety and risk assessment problem of the spindle systems has been considered in order to extend the equipment life and improve the economic benefit. After summing-up the uncertain factors that mainly influence reliability allocation of the spindle system, a multi-hierarchic structure is established based on the Fuzzy Analytic Hierarchy Process (FAHP). Using the weak compactness of the unit sphere in Hilbert space, this paper puts forward the standard Hilbert's index sub-space in order to perform the safety index evaluation and to set up analytical model in the context of vector norms in Hilbert apace. Meanwhile, combining the weight calculated by FAHP with the proposed model, the degree of the contribute rate of each unit in the spindle system is obtained and then the unit which is important or more important can be evaluated by means of index analysis and horizontal and vertical comparison, resulting in maintaining the critical components of the complex systems.