  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.
