Stage-independent multiple sampling plan by variables inspection for lot determination based on the process capability index C_pk

Abstract

Multiple sampling plan (MSP) has been proved that the sample units required for inspection at each stage are usually smaller than the conventional single or double sampling. However, it is more complex to administer and difficult to derive the corresponding operating characteristic function since the judgment on the submitted lot under the MSP is not only dependent on the result of current sampling but also on previous sampling results. Thus, this paper attempts to provide a relaxed type of conventional MSP by assuming the sampling inspection at each stage is independent which is called variables stage-independent multiple sampling plan and integrated with the most widely-used process capability index C_pk. For the cost-efficient purpose, the plan parameters are solved under an optimisation model that minimises the average sample number by satisfying the required quality levels and tolerated risks. Finally, the applicability of the proposed plan is illustrated in a case study.

KEYWORDS:

• Acceptance sampling
• average sample number
• process capability indices
• sampling plans
• operating characteristic function

Acknowledgements

The authors would like to thank the Associate Editor and three anonymous referees for their helpful comments and careful readings, which significantly improved the presentation of this paper.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the Ministry of Science and Technology of Taiwan [grant number MOST 108-2218-E-167-008-MY2] and also supported by Lembaga Pengelola Dana Pendidikan Indonesia (LPDP Indonesia, scholarship ID reference number Armin Darmawan: 2020032230686).

Notes on contributors

Chien-Wei Wu

Chien-Wei Wu is currently a Distinguished Professor in the Department of Industrial Engineering and Engineering Management at National Tsing Hua University (NTHU), Taiwan. Dr Wu received his Ph.D. degree in Industrial Engineering and Management with Outstanding Ph.D. Student Award from National Chiao Tung University in 2004 and the M.S. degree in Statistics from NTHU in 2002. Dr Wu has received Dr Ta-You Wu Memorial Award (Outstanding Young Researcher Award) from National Science Council (NSC) in 2011, Outstanding Young Industrial Engineer Award from Chinese Institute of Industrial Engineers (CIIE) in 2011, and Outstanding Research Award from the Ministry of Science and Technology (MOST) in 2021. He is also serving as one of Editors-in-Chief of Quality Technology and Quantitative Management (QTQM) and editorial board members for several international journals. His research interests include quality engineering and management, statistical process control, process capability analysis and data analysis.

Armin Darmawan

Armin Darmawan is currently a Ph.D. student in the Department of Industrial Engineering and Engineering Management at National Tsing Hua University (NTHU), Taiwan. Besides, Armin Darmawan is a lecturer in the Department of Industrial Engineering, Hasanuddin University, Indonesia. Armin Darmawan received a master's degree in Industrial Engineering from the University of Indonesia in 2011. His research interests include quality engineering and management, risk management, statistical process control, process capability analysis, and data analysis. Armin Darmawan has received award LPDP scholarship from Indonesia Government in 2020.

Shih-Wen Liu

Shih-Wen Liu is currently an Assistant Professor in the College of Management at National Chin-Yi University of Technology (NCUT), Taiwan. Dr Liu received his Ph.D. degree in Industrial Management from National Taiwan University of Science and Technology (NTUST) in 2016. Dr Liu was honourably subsidised by Ministry of Science and Technology (MOST) of Taiwan to Rutgers University for research purposes. Before he joined NCUT, Dr Liu was an R&D engineer in the contact lens industry which expands his horizon of the Industrial Engineering field. Also, Dr Liu was a member of Quality Management Lab in National Tsing Hua University (NTHU), Taiwan as a Postdoctoral Researcher. His research interests include quality engineering and management, statistical process control, process capability analysis, applied statistics, and data analysis.