Learning curves for processes generating defects requiring reworks

The earliest learning curve representation is due to Wright, and is a geometric progression that expresses the decreasing time required to accomplish a repetitive operation. The theory in its most popular form states that as the total quantity of units produced doubles, the time per unit declines by some constant percentage. Wright's model assumes that all units produced are of acceptable quality. However, in many practical situations, there is a possibility that the process goes out-of-control, thus, producing defective items that need to be reworked. Then, the rework time per unit must be accounted for when measuring the learning curve. This paper does so, and a modification of Wright's learning curve is presented for processes that generate defects that can be reworked. However, it is worth mentioning that the work presented herein has two limitations. Firstly, this paper does not apply to cases when defects are discarded. Secondly, this paper assumes the rate of generating defects is constant, which means that the production process does not benefit from any changes for eliminating the defects. Analytical results show that the learning curve, under some conditions, could be of a convex form. Furthermore, this paper provides a plausible explanation to the plateauing phenomenon that intrigued several researchers.