Generalization of usual capability indices for unilateral tolerances

Capability indices are dimensionless quantities measuring the aptitude of a process to manufacture items whose characteristics must be within a specified tolerance ranges. The usual indices $C_p$, $C_{pk}$, $C_{pm}$, and $C_{pmk}$ are used for a process of normal distribution and a target located at the center of the tolerance interval. Various indices derived from the previous family allow to consider more complex situations when asymmetrical tolerances and non-normal distributions are taken into account. In this paper we study the case where a single tolerance is imposed because the shifts in the direction of this tolerance appear much more serious than in the opposite direction. We propose a family of four indices having interpretations and properties similar to those of the usual family.