This study was carried out to minimize the lifting force and to design the slim sized frame of a height adjustment mechanism. This unit is designed for the display devices in order to enhance the ergonomics for effective height adjustment as well as to achieve much slimmer frame for the pedestal. A tolerance analysis of 6 sigma was applied to achieve smooth lift at design stage not to change the tolerance specification of gap several times in a roller type of lifting mechanism at mass production stage. The specification of minimum gap and the target of production yield ratio were agreed with a quality team before tooling. A DFSS simulation on drawings had been done with reasonable tolerance and achievable standard deviation(${sigma}$) several times until the target specification of gap and yield ratio was met. Once tolerance and deviation(${sigma}$) were fixed tooling start was done successfully. A CAE method was applied to achieve a slim design. Design parameters were frozen when those parameters matched the reference strength data of standard model. Through those tolerance analysis and CAE simulation the number of tool modification was reduced and production yield ratio was raised up without arguing quality specification at production stage in the end.