Estimation of the Six Sigma Quality Index

Chun-Chieh Tseng, Kuo-Ching Chiou and Kuen-Suan Chen ()
Additional contact information
Chun-Chieh Tseng: School of Internet Economics and Business, Fujian University of Technology, Fuzhou 350014, China
Kuo-Ching Chiou: Department of Finance, Chaoyang University of Technology, Taichung 413310, Taiwan
Kuen-Suan Chen: Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan

Mathematics, 2022, vol. 10, issue 19, 1-13

Abstract: The measurement of the process capability is a key part of quantitative quality control, and process capability indices are statistical measures of the process capability. Six Sigma level represents the maximum achievable process capability, and many enterprises have implemented Six Sigma improvement strategies. In recent years, many studies have investigated Six Sigma quality indices, including Q p k . However, Q p k contains two unknown parameters, namely δ and γ , which are difficult to use in process control. Therefore, whether a process quality reaches the k sigma level must be statistically inferred. Moreover, the statistical method of sampling distribution is challenging for the upper confidence limits of Q p k . We address these two difficulties in the present study and propose a methodology to solve them. Boole’s inequality, Demorgan’s theorem, and linear programming were integrated to derive the confidence intervals of Q p k , and then the upper confidence limits were used to perform hypothesis testing. This study involved a case study of the semiconductor assembly process in order to verify the feasibility of the proposed method.

Keywords: Six Sigma quality index; linear programming; estimations; upper confidence limit; statistic hypothesis testing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/19/3458/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/19/3458/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:19:p:3458-:d:922413

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().