Fuzzy Estimations of Process Incapability Index

Abstract

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 ((C) over tilde (pp)), fuzzy process mean ((mu) over tilde) and fuzzy variance ((sigma) over tilde (2)), which are obtained by using the fuzzy extension principle, are used together with fuzzy SLs (S (L) over tildes) and fuzzy target value ((T) over tilde). In order to find the membership functions of fuzzy inaccuracy index ((C) over tilde (ia)) and fuzzy imprecision index ((C) over tilde (ip)), the alpha-cuts of the fuzzy observation are employed. Then the fuzzy estimations of the index (C) over tilde (pp) are produced for triangular fuzzy numbers (TFN). The proposed index (C) over tilde (pp) is applied in a piston manufacturer firm.