Capability indices are dimensionless quantities measuring the ability of a process to manufacture items whose characteristics must be within a specified tolerance range. In this case and for a normally distributed process, the indices ,and pmk are widely used. In this paper we study the case where a single tolerance is imposed because the shifts in the direction of this tolerance seem more serious than in the opposite direction. We propose a family of four indices having better properties than the existing indices. These new indices are created from the usual properties and interpretations of the indicesand , pmk C and can be used without difficulty in industry.
For a process normally distributed and a target located at the mid-point of a twosided tolerance interval, Vännman suggests a family of indices depending on two parameters. In order to choose the parameters which allow to obtain an index that is sensitive to departures of the mean from the target, we need to take the properties of its estimator into account. For a target not located at the mid-point of the interval of tolerance, Chen and Pearn suggest a family of indices generalizing Vännman's. The moments of these indices are given, then their expected values and mean square errors are studied to choose an index that is sensitive to the deviations of the mean from the target.
For a non-normal Pearsonian population, Clements suggests a method to estimate the usual capability indices p C and pk C . Pearn and Kotz apply this method to the pm C and pmk C indices. However these considerations only apply to the case of symmetrical tolerances. . In this paper, a geometrical interpretation of these last indices is proposed and, from this approach, new indices are suggested for a non-normal population and for asymmetrical tolerances.
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