Abstract
Process capability analysis (PCA) is an important statistical analysis approach for measuring and analyzing the ability of the process to meet specifications. This analysis has been applied by producing process capability indices (PCIs). \({C}_{p}\) and \({C}_{pk}\) are the most commonly used PCIs for this aim. Although they are completely effective statistics to analyze process’ capability, the complexity of the production processes based on uncertainty arising from human thinking, incomplete or vague information makes it difficult to analyze the process capability with precise values. When there is uncertain, complex, incomplete and inaccurate information, the capability of the process is successfully analyzed by using the fuzzy sets. Neutrosophic sets (NSs), one of the new fuzzy set extensions, have a significant role in modeling uncertainty, since they contain the membership functions of truth, indeterminacy, and falsity definitions rather than an only membership function. This feature provides a strong advantage for modeling uncertainty. In this paper, PCA has been performed based on NSs to overcome uncertainties of the process. For this purpose, specification limits (SLs) have been reconsidered by using NSs and two of the well-known process capability indices (PCIs) named \({C}_{p}\) and \({C}_{pk}\) have been reformulated. Finally, the neutrosophic process capability indices (NPCIs) named \({C}_{p}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{p}\right)\) and \({C}_{pk}\) \(\left({\tilde{\stackrel{⃛}{C}}}_{pk}\right)\) have been derived for three cases that are created by defining SLs. Additionally, the obtained NPCIs have also been applied and confirmed on real case problems from automotive industry. The obtained results show that the NPCIs support the quality engineers to easily define SLs and obtain more flexible and realistic evaluations for PCA.
CAPABILITY INDICES FOR CONTROL CHARTS BASED ON REGRESSION MODELS
