Abstract: The fuzziness existing in the rational value of the tool life is analyzed and the rational value of the tool life is taken as a fuzzy variable. The fuzzy restriction and the possibility distribu- tion function of the rational value of the tool life is given out based on possibility theory. After considering the fuzziness existing in the rational value of the tool life, allowable interval of the rational value of the tool life should become a fuzzy allowable interval. According to fuzzy set theory, the fuzzy allowable interval of the rational value of the tool life is defined and its membership func- tion is derived. Then, formulae to calculate reliability tool life is proposed based on fuzzy probability theory. Finally real example is carried out. The real example shows that the fuzzy probability can reflect effectively the fuzzy working state of the cutting tool and avoid and reduce the economic lost of compulsive changing tool.

Key words: Fuzzy allowable interval, Possibility theory, Reliability, Tool life