In many manufacturing processes, unbalanced tolerance design is a common occurrence. It occurs when the deviation of a quality characteristic in one direction is more harmful than in the opposite direction. The failure mode in these two directions is usually different. Furthermore, automatic inspection and measurement technology are widely used by the industries. The nonconforming part will be detected automatically. Thus, a truncated asymmetrical quadratic loss function is assumed for the unbalanced tolerance design. Traditionally, the manufacturer would either choose the smaller tolerance as the tolerance for both sides, or would set the process mean at the middle of the tolerances. Both methods fail to minimise the expected quality loss. The purpose of this paper is to find out the optimal manufacturing setting such that the expected quality loss is minimised. The results show that the process mean should be shifted a little from the target value.Notation y quality characteristic l process mean of a quality characteristic r standard deviation of a quality characteristic L(y) quality loss function of a quality characteristic, y T target value of a quality characteristic D one side tolerance of a symmetrical specification A quality loss at the specification limits of a symmetrical quality loss function k coefficient of a symmetrical quality loss function k 1 coefficient of an asymmetrical quality loss function on the left-hand side k 2 coefficient of an asymmetrical quality loss function on the right-hand side R k asymmetrical ratio of the coefficient of the quality loss function, i.e. R k =k 1 /k 2 D 1 tolerance on the left-hand side of an unbalanced tolerance D 2 tolerance on the right-hand side of an unbalanced tolerance A 1 quality loss at the specification limit on the left hand side for an unbalanced tolerance design A 2 quality loss at the specification limit on the right hand side for an unbalanced tolerance design R A quality loss ratio at the specification limits, i.e. R A =A 1 /A 2 L(d, A 1 , A 2 ) expected quality loss as a function of d, A 1 and A 2 d standardised distance of the process mean apart from target value, i.e. d= (lÀT)/r l o optimal process mean that minimises expected quality loss d o optimal standardised distance of the process mean apart from target value, i.e. d o =(l o ÀT)/r USL upper specification limit LSL lower specification limit C p process capability ratio, i.e. C p = (USLÀ LSL)/6r R L quality loss ratio, i.e. R L =EL (0)/EL(d o ) AR A (actual value of R A )/(estimating value of R A ) AR k (actual value of R k )/(estimating value of R k ) d o * standardised distance of the process mean apart from target value computed by the actual values of R k and R A Err_d o error ratio of d o , i.e. Err_d o =(d o * Àd o )/d o

No abstract

No abstract