Optimal set-up of a manufacturing process with unequal revenue from oversized and undersized items

The optimal level to which the mean of a critical variable should be set-up, when the revenue per unit of oversized and undersized items are unequal, has been determined for the case where the variable is distributed normally. It has been proven analytically that the optimal set-up level should not be in the middle in-between the specification limits, but at a certain distance from it in the direction of the type of non-conforming item which generates a higher economic value per unit. That optimal distance was determined to depend on the spread of the specification limits, and on the relationship between the unit revenues obtained from oversized and undersized items. The use of the optimal set-up level is facilitated by the derivation of a simple closed-form formula. The increase in profit - with optimal set-up - was found to reach up to about ten percent when the spread of the specification limits is narrow. Sensitivity of the profit to use of non-optimal set-up levels was investigated.