In the machining processes the characteristics which have skew distributions are often observed. In evaluating their process capability, the method for the normal distribution is generally appled, and usually the process capability index (Cp) is used. However, if the distribution is not normal, the index has a different meaning and the process capability cannot be evaluated correctly. In this paper, a problem when the Cp is used for the skew distributions is pointed out firstly, and secondly a new evaluation method for the skew distributions is proposed. This method is to adjust Cp using Cornish-Fisher expansion. The actual procedure is described with an example, and a comparison with other methods is made. This method corresponds to the one for the normal distribution, so the evaluation can be done in the conventional way of thinking. Moreover, this method has merits that it is not necessary to specify the type of the distribution nor to make troublesome calculation.

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