Estimating Some Metrics in Six Sigma Through Confidence Intervals
Abstract
Purpose: This paper suggests a methodology for estimating some Six Sigma metrics using confidence intervals.
Methodology/Approach: This approach assumes that the process follows a normal distribution with a constant variance. The mean of the process is shifted from the target value to the right or left by 1.5 standard deviations. The estimates are based on a random sample of size n taken during a time when the process is stable.
Findings: The paper describes how to create confidence intervals for the number of defects per unit, the probability that a unit will be free of defects, and the rolled throughput yield.
Research Limitation/implication: We assume a discrete process in which n units of the product are selected during a time when the process is stable.
Originality/Value of paper: By applying the proposed estimation procedures, process performance evaluations can be improved, facilitating decision-making for Six Sigma projects.
Full text article
References
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.
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.
ISO 13053 – 1, 2011. Quantitative methods in process improvement ̶ Six Sigma ̶ Part 1: DMAIC methodology. Geneva: ISO copyright office.
Le, H., Duffy, G., 2023. Human-Centered Lean Six Sigma. Creating a Culture of Integrated Operational Excellence. New York: Routledge.
Miller, I., Miller, M., 2014. John E. Freund's Mathematical Statistics with Applications. Eighth Edition. Harlow: Pearson Education Limited.
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.
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.
Terek, M. and Hrnčiarová, Ľ., 2004. Štatistické riadenie kvality. Bratislava: Iura Edition.
Terek, M., 2023a. Charakteristiky výkonnosti procesu v metodológii Six Sigma. Slovenská štatistika a demografia, 33(4), pp. 20 – 40. Avalaible at: https://ssad.statistics.sk/SSaD/wp-content/files/4_2023/4_2023_SSaD_clanok_2_Terek.pdf.
Terek, M., 2023b: How to Estimate the Sigma Level of the Process. Quality Innovation Prosperity 27(3). https://doi.org/10.12776/qip.v27i3.1947.
Authors
Copyright (c) 2024 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.