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‎Process capability indices are used widely throughout the world to give a quick indication of a process capability in a format that is easy to use and understand‎. ‎A process capability index $C_p$ that constructed for measuring the quality is an effective tool for assessing process capability‎, ‎since this index can reflect whether a centering process is capable of reproducing items meeting the specifications limits‎. ‎The minimax approach is proposed in this paper for testing capability on the basis of precision index Cp when the producer goal is avoiding the largest possible risk‎. ‎Motivations and benefits of proposing minimax approach are discussed for capability test‎. ‎Also‎, ‎the proposed method clarified by an industrial application.