Fuzzy estimations of process incapability index

Process capability indices (PCIs) provide numerical measures on whether a process confirms to the defined manufacturing capability prerequisite. In the literature, some PCIs have been used to measure the ability of process to decide how well the process meets the specification limits (SLs). These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. In this paper, one of the most important PCIs, process incapability index ( ) (C_pp) which provides more process information than other process PCIs and is easily applied is analyzed together with the indices inaccuracy ((C_ia) and imprecision ((C_ip). In this paper, the index (C_pp) is also analyzed by using the fuzzy set theory to obtain a deep and flexible analysis. To produce fuzzy process incapability index ((C̃_pp), fuzzy process mean (μ̃ _pp) and fuzzy variance ((σ̃ _pp), which are obtained by using the fuzzy extension principle, are used together with fuzzy SLs ((SL̃%s)) and fuzzy target value ((T̃). In order to find the membership functions of fuzzy inaccuracy index ((C̃_ia) and fuzzy imprecision index ( (C̃_ip), the α-cuts of the fuzzy observation are employed. Then the fuzzy estimations of the index pp C% are produced for triangular fuzzy numbers (TFN). The proposed index (C̃_pp) is applied in a piston manufacturer firm.