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    Design and Analysis of Cpm and Cpmk Indices for Uncertainty Environment by Using Pythagorean Fuzzy Sets
    (Institute of Electrical and Electronics Engineers Inc., 2022) Yalcin S.; Kaya I.
    Process capability analysis (PCA) is a statistical analysis tool to examine variability of the process that causes faults for outputs and reduces customer satisfaction level. So, it is a completely effective method to improve the process' quality. One of the effective methods is process capability indices (PCIs) that are used to analyze the capability of any process by using specification limits (SLs) and process' variation. Especially in real case problems, there are many factors that causing uncertainty for the process. Although traditional PCIs are effective tools to analyze variation of process, they caused some misleading results and incorrect interpretations when the process has uncertainties. To overcome the problem, the PCIs have been re-designed under uncertainty to increase their effectiveness by using fuzzy sets (FSs). In recently, some fuzzy set extensions (FSEs) have been derived to deal with uncertainty and they can model uncertainties of process more effectively. In this paper, Pythagorean Fuzzy Sets (PFSs), one of the most common FSEs, are used to analyze process capability bu improving some PCIs based on PFSs. For this aim, generally used PCIs called Cpm and Cpmk are re-designed by using PFSs as the first time in the literature. The mathematical structures of these two indices are re-formulated and PCIs based on PFSs (PFPCIs) have been derived. Additionally, an application related with dimensions of a gear for a piston is also applied to analyze usage of proposed PFPCIs. The obtained results confirmed that the indices Cpm and Cpmk based on PFSs are more capable for modelling uncertainty and give more information and have more sensitiveness than the traditional PCIs. © 2022 IEEE.
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    Two-Dimensional Uncertainty Analysis for Cp and Cpk Process Capability Indices
    (Institute of Electrical and Electronics Engineers Inc., 2022) Yalcin S.; Kaya I.
    Process capability analysis (PCA) is an efficient statistical technique for calculating of process' ability to meet predetermined specification limits (SLs) that defined by customer, engineers or designers. Measurements and evaluations for PCA may be vague, incomplete or inaccurate in the real-case problems. In that cases, the process capability should be successfully measured by using fuzzy set extensions to model uncertainties of the process. One of fuzzy set extensions named Pythagorean fuzzy Sets (PFSs) that also contains the non-membership function can be employed as an effective tool to model uncertainty better than traditional fuzzy sets (TFSs). In this paper, a novel approach based on PFSs is suggested to increase flexibility and sensitivity of the PCA and to successfully model the uncertainties. For this aim, two of frequently used process capability indices (PCIs) Cp and Cpk, are analyzed based on PFSs. Then, the Pythagorean fuzzy process capability indices (PFPCIs) have been derivate respectively for the indices Cp and Cpk and the mathematical backgrounds of these indices have been developed for the first time in the literature. Additionally, the proposed indices Cp and Cpk have been applied to a real case problem from manufacturing industry. The obtained PCIs based on PFSs provide some additional flexibility and information about the process since they better modeled process uncertainty. Moreover, it is demonstrated that the proposed PFCPIs can be effectively applied on process to manage PCA. © 2022 IEEE.