For assembly of rotating machines, such as machining tools, industrial turbomachinery, or aircraft gas turbine engines, parts need to be assembled in order to avoid internal bending of the geometric axis of the rotor to meet functional and vibration requirements. Straight-build assembly optimization is a way of joining parts together in order to have a straight line between the centers of the components. Straight-build assembly is achieved by minimizing eccentricity error stage-by-stage in the assembly. To achieve minimal eccentricity, this paper proposes three assembly procedures: (i) table-axis-build assembly by minimizing the distances from the centers of components to table axis; (ii) minimization of the position error between actual and nominal centers of the component; and (iii) central-axis-build assembly by minimizing the distances from the centers of components to a central axis. To test the assembly procedures, two typical assembly examples are considered using four identical rectangular components and four nonidentical rectangular components, respectively. Monte Carlo simulations are used to analyze the tolerance build-up, based on normally distributed random variables. The results show that assembly variations can be reduced significantly by selecting best relative orientation between mating parts. The results also show that procedures (i) and (ii) have the most potential to minimize the error build-up in the straight build of an assembly. For these procedures, the variation is reduced by 45% and 40% for identical and nonidentical components, respectively, compared to direct-build assembly. Procedure (iii) provides better performance than direct-build assembly for identical components assembly, while it gives smaller variation at the first two stages and larger variation at the third stage for nonidentical components assembly. This procedure could be used in an assembly with limited stages.