{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:00:22Z","timestamp":1777705222547,"version":"3.51.4"},"reference-count":34,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,1,10]]},"abstract":"<jats:p>Process capability analysis (PCA) is an important stage to check variability of process by using process capability indices (PCIs) that are very effective statistics to summarize process\u2019 performance. Traditional PCIs can produce some incorrect results and declare misinterpretation about process\u2019 quality if the process includes uncertainties. Additionally, definitions of process\u2019 parameters with exact values is not possible when there are uncertainty caused by measurement errors, sensitivities of measuring instruments or quality engineers\u2019 hesitancies. Although the fuzzy set theory (FST) has been successfully used in PCA, it is the first time to use of Pythagorean fuzzy sets (PFSs) to model uncertainties of process more than traditional fuzzy sets in PCA. Since the PFSs has two-dimensional configurations by defining membership and non-membership values, they also have a huge ability to model uncertainty that arises from the human\u2019s thinking and hesitancies, and has brought flexibility, sensitivity and reality for PCA. In this paper, specification limits (SLs), mean (\u03bcp), standard deviation (\u03c3) and target value (T) main parameters of PCIs have been analyzed by using PFSs and Pythagorean fuzzy process capability indices (PFPCIs) for two well-known PCIs such as ( C \u02dc pm ) and ( C \u02dc pmk ) have been derived. The Pythagorean ( C \u02dc pm ) and ( C \u02dc pmk ) indices have also been applied and tested on some numerical examples based on real case applications from manufacturing industry. The obtained results show that PFPCIs provide wider knowledge about capability of process and to obtain more realistic results. As a result of considering all possibilities about the process, it has been concluded that the process is incapable. In light of this information, the results obtained using different fuzzy set extensions for (Cpm) and (Cpmk) indices can be compared.<\/jats:p>","DOI":"10.3233\/jifs-234683","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T11:55:45Z","timestamp":1701431745000},"page":"2331-2355","source":"Crossref","is-referenced-by-count":3,"title":["Design and analysis of Cpm and Cpmk indices for uncertainty environment by using two dimensional fuzzy sets"],"prefix":"10.1177","volume":"46","author":[{"given":"Selin","family":"Yal\u00e7\u0131n","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, \u0130stanbul Beykent University\/Faculty of Engineering-Architecture, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0130hsan","family":"Kaya","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Y\u0131ld\u0131z Technical University\/Faculty of Mechanical Engineering, Turkey"},{"name":"Precidency of the Republic of T\u00fcrkiye, Defence Industry Agency, Ankara, Turkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"6","key":"10.3233\/JIFS-234683_ref1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1002\/qre.4680070602","article-title":"Process capability indices-an overview of theory and practice","volume":"7","author":"Porter","year":"1991","journal-title":"Quality and Reliability Engineering International"},{"key":"10.3233\/JIFS-234683_ref3","doi-asserted-by":"crossref","unstructured":"Pearn W.L. , Kotz S. and Johnson N.L. , Distributional and inferential properties of process capability indices, J Qual Technol, 24(4) (1992), 216\u2013231.","DOI":"10.1080\/00224065.1992.11979403"},{"issue":"5","key":"10.3233\/JIFS-234683_ref4","doi-asserted-by":"crossref","first-page":"3963","DOI":"10.1520\/JTE20180038","article-title":", A Literature Review on Fuzzy Process Capability Analysis","volume":"48","author":"Kaya","year":"2020","journal-title":"Journal of Testing and Evaluation"},{"issue":"1","key":"10.3233\/JIFS-234683_ref5","first-page":"13","article-title":"Design and analysis of process capability indices Cpm and Cpmk by neutrosophic sets","volume":"19","author":"Yalc\u0131n","year":"2022","journal-title":"Iranian Journal of Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-234683_ref6","first-page":"1049","article-title":"What can fuzziness do for capability analysis based on fuzzy data","volume":"28","author":"Chen","year":"2021","journal-title":"Scientia Iranica"},{"issue":"1","key":"10.3233\/JIFS-234683_ref8","doi-asserted-by":"crossref","first-page":"477","DOI":"10.3233\/JIFS-219205","article-title":"Process design and capability analysis using penthagorean fuzzy sets: surgical mask production machines comparison","volume":"42","author":"Haktan\u0131r","year":"2022","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"6","key":"10.3233\/JIFS-234683_ref9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s40314-022-01973-5","article-title":"Analyzing of process capability indices based on neutrosophic sets","volume":"41","author":"Yalc\u0131n","year":"2022","journal-title":"Computational and Applied Mathematics"},{"issue":"631","key":"10.3233\/JIFS-234683_ref10","first-page":"1","article-title":"Inspection plan based on the process capability index using the neutrosophic statistical method","volume":"7","author":"Aslam","year":"2019","journal-title":"Mathematics"},{"issue":"2","key":"10.3233\/JIFS-234683_ref13","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1007\/s12351-019-00490-4","article-title":"A process capability index for normal random variable with intuitionistic fuzzy information","volume":"21","author":"Hesamian","year":"2021","journal-title":"Operational Research"},{"issue":"3","key":"10.3233\/JIFS-234683_ref14","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.3233\/JIFS-141877","article-title":"Onar and B. 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