Entire product capability analysis chart with asymmetric tolerances index Spa

Chun-Min Yu; Kun-Tzu Yu; Kuen-Suan Chen; Chun-Min Yu; Kun-Tzu Yu; Kuen-Suan Chen

doi:10.3934/mbe.2020387

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7605-7620. doi: 10.3934/mbe.2020387

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Entire product capability analysis chart with asymmetric tolerances index S_pa

1.
Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411, Taiwan, R. O. C
2.
Department of Marketing and Distribution Management, Tzu Chi University of Science and Technology, Hualien 970, Taiwan, R. O. C
3.
Department of Business Administration, Chaoyang University of Technology, Taichung 41349, Taiwan, R. O. C

Received: 05 August 2020 Accepted: 26 October 2020 Published: 03 November 2020

This study proposes the S_pa-product capability analysis chart (S_pa-PCAC), which can widely represent multiple process capabilities with asymmetric tolerances of Smaller-the-Better, Larger-the-Better, and Nominal-the-Best characteristics. Process capability index S_pa is generated based on index S_pk, which uses asymmetric tolerances to reasonably measure process capabilities. The interval estimates of the indices are derived to reliably assess process capabilities. The Six-Sigma-based quality-level and its connection with the process yield are introduced in the capability zone of S_pa-PCAC to check if the process capabilities can meet the requirements. One example of an entire product is given for application.
- product capability analysis chart,
- process capability index,
- asymmetric tolerances,
- capability zone,
- Six-Sigma
Citation: Chun-Min Yu, Kun-Tzu Yu, Kuen-Suan Chen. Entire product capability analysis chart with asymmetric tolerances index Spa[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7605-7620. doi: 10.3934/mbe.2020387

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Abstract

This study proposes the S_pa-product capability analysis chart (S_pa-PCAC), which can widely represent multiple process capabilities with asymmetric tolerances of Smaller-the-Better, Larger-the-Better, and Nominal-the-Best characteristics. Process capability index S_pa is generated based on index S_pk, which uses asymmetric tolerances to reasonably measure process capabilities. The interval estimates of the indices are derived to reliably assess process capabilities. The Six-Sigma-based quality-level and its connection with the process yield are introduced in the capability zone of S_pa-PCAC to check if the process capabilities can meet the requirements. One example of an entire product is given for application.

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