How to Estimate the Sigma Level of the Process
DOI:
https://doi.org/10.12776/qip.v27i3.1947Keywords:
Six Sigma, defects per milion opportunities, random sample, confidence intervalAbstract
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.
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.
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