Abstract
Purpose: This paper proposes a procedure for estimating the sigma level of the process through a confidence interval.
Methodology/Approach: The approach is based on a model in which the process has a normal distribution and constant variance, and its mean is shifted to the right or left by 1.5 standard deviations.
Findings: The paper explains a method for creating a random sample along with determining the sample size to estimate the “defects per million opportunities” characteristic through a confidence interval. Based on it, the confidence interval for the “sigma level” of the process is determined.
Research Limitation/implication: We assume a discrete process in which n pieces of the product are selected. The proposed procedure assumes that the process is in statistical control.
Originality/Value of paper: Applying the proposed random sampling and estimation procedure can improve evaluations of process performance, aiding decision-making for Six Sigma projects.
Full text article
References
Allen, T. T., 2019. Introduction to Engineering Statistics and Lean Six Sigma. Statistical Quality Control and Design of Experiments and Systems. Third Edition. London: Springer.
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J. and Ohlmann, J. W., 2020. Statistics for Business and Economics. 14e Edition. Boston: Cengage Learning, Inc.
Antony, J., Vinodh, S. and Gijo, E. V., 2016. Lean Six Sigma for Small and Medium Sized Enterprises. A Practical Guide. Boca Raton: Taylor & Francis Group.
Bass, I., 2007. Six Sigma Statistics with Excel and Minitab, New York: McGraw-Hill.
Bass, I., and Lawton, B., 2009. Lean Six Sigma Using SigmaXL and Minitab. New York: McGraw-Hill.
Basu, R., 2009. Implementing Six Sigma and Lean: A Practical Guide to Tools and Techniques. Oxford: Elsevier Ltd.
Bhakri, S., 2023. (DPMO) Defects per Million Opportunities: Simplified With Example. [online] Available at: https://www.isixsigma.com/dictionary/defects-per-million-opportunities-dpmo/, [9 November 2023].
Bloom, D. T., 2022. Achieving HR Excellence through Six Sigma. Second Edition. Boca Raton: Routledge.
Gitlow, H. S., Melnyck, R. J. and Levine, D. M., 2015. A Guide to Six Sigma and Process Improvement for Practitioners and Students. Foundations, DMAIC, Tools, Cases, and Certification. Second Edition. Old Tappan: Pearson Education, Inc.
Le, H., Duffy, G., 2023. Human-Centered Lean Six Sigma. Creating a Culture of Integrated Operational Excellence. New York: Routledge.
ISO 13053 – 1, 2011. Quantitative methods in process improvement ̶ Six Sigma ̶ Part 1: DMAIC methodology. Geneva: ISO copyright office.
ISO 13053 – 2, 2011, Quantitative methods in process improvement ̶ Six Sigma ̶ Part 2: Tools and techniques. Geneva: ISO copyright office.
ISO 22514-3, 2020. Statistical methods in process management — Capability and performance — Part 3: Machine performance studies for measured data on discrete parts. Geneva: ISO copyright office.
Meran, R., John, A., Roenpage, O. and Staudter, Ch., 2013. Six Sigma + Lean Toolset. Mindset for Successful Implementation of Improvement Projects. Second Edition. Berlin Heidelberg: Springer-Verlag.
Montgomery, D. C., 2013. Introduction to Statistical Quality Control. Seventh edition. Hoboken: J. Wiley and Sons.
Patel, S., 2016. The Tactical Guide to Six Sigma Implementation. Boca Raton: Taylor & Francis Group.
Pillet, M., 2005. Six Sigma Comment l'appliquer. Deuxième tirage. Paris: Éditions d’Organisation.
Pyzdek, T., 2003. The Six Sigma Handbook. Revised and Expanded. A Complete Guide for Green Belts, Black Belts, and Managers at All Levels. New York: McGraw-Hill.
Pyzdek, T. and Keller, P. A., 2010. The Six Sigma handbook. A Complete Guide for Green Belts, Black Belts, and Managers at All Levels. Third Edition. New York: McGraw-Hill Companies, Inc.
Sproull, B., 2019. Theory of Constraints, Lean, and Six Sigma Improvement Methodology. Making the Case for Integration. New York: Routledge/Productivity Press.
Stamatis, D. H., 2003. Six Sigma for Financial Professionals. Hoboken: J. Wiley and Sons.
Terek, M. and Hrnčiarová, Ľ., 2004. Štatistické riadenie kvality. Bratislava: Iura Edition.
Terek, M., 2017a. Interpretácia štatistiky a dát. 5. doplnené vydanie. Košice: Equilibria.
Terek, M., 2017b. Interpretácia štatistiky a dát. Podporný učebný materiál. 5. doplnené vydanie. Košice: Equilibria.
Terek, M., 2019. Dotazníkové prieskumy a analýzy získaných dát. 1. vydanie. Košice: Equilibria.
Terek, M., 2023b. Charakteristiky výkonnosti procesu v metodológii Six Sigma. Slovenská štatistika a demografia, číslo 4/2023.
Authors
Copyright (c) 2023 Milan Terek
This work is licensed under a Creative Commons Attribution 4.0 International License.
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. This journal is licensed under a Creative Commons Attribution 4.0 License - http://creativecommons.org/licenses/by/4.0.
Authors who publish with the Quality Innovation Prosperity agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.