s. yalcin

Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ2) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and  sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more  broadly more flexibility. For this aim, the main parameters of PCIs have been defined  and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as Csp, Cspk, Cfp and Cfpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic,  more sensitive, and more comprehensive results.

Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices  C_{pm}  and  C_{pmk}  have been developed to consider customers' ideal value that called target value ( T ). Although, these indices have similar features of the well-known indices C_{p}  and  C_{pk} , one of the most important differences is to consider textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices  C_{pm} and C_{pmk} have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) widetilde{dddot{C}}_{pm} and widetilde{dddot{C}}_{pmk} have been obtained and the main formulas of them have been produced. Additionally, the proposed widetilde{dddot{C}}_{pm} and widetilde{dddot{C}}_{pmk} have been applied on real case studies from manufacturing industry. The obtained results show that the indices widetilde{dddot{C}}_{pm} and widetilde{dddot{C}}_{pmk} include more informative and flexible results to evaluate capability of process.