Flatness failures include center buckles and edge waves. With the former, the center of the width is excessively elongated, resulting in waviness, while with the latter, the edges of the strip are excessively elongated,resulting again in waviness. Flatness failures and strip crowns are caused by widthwise differences in the thickness reduction rate. General methods for reducing strip crown include the 4-high rolling mill, in which the work rolls are supported by back-up rolls; the use of a roll crown, in which the work roll is given a convex shape; and the use of the roll bender to deflect the roll in the direction opposite that of the predicted strip crown. All these methods have the following aims: Before entry of the strip into the rolls, the work roll gap is arranged to have a concave shape so that the center of the strip width is thinner than edges, and after entry of the strip, the surfaces of the top and bottom work rolls become parallel as a consequence of rolling. These methods are in practical use, and strip crown has progressively improved. New methods have also been developed for further improvements. These include the roll-shifting mill, in which the rolls are shifted in the widthwise direction, and the roll-cross mill, in which the roll axes are crossed. There are two types of roll-shifting mill. One shifts the work rolls, and the other shifts the intermediate rolls. The work-roll shifting type aims to make the strip thickness uniform and improve the flatness over a wide range of strip widths by shifting rolls of special shapes, as shown in the figure. The intermediate-roll shifting type aims at greater efficiency in achieving the same objectives by shifting the intermediate rolls so that their barrel ends approach the edges of the material being rolled. In some cases, a special shape is also given to the intermediate rolls. In the roll-cross mill, the top and bottom roll axes are positioned obliquely to each other to adjust the roll gap. A large effect can be obtained with a crossing angle as small as 1.5. The three types of roll-cross mill are shown in the figure. The pair-roll-cross mill is commonly used in hot rolling mills for plate and strip.