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Variables skip-lot sampling plans on the basis of process capability index for products with a low fraction of defectives

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Abstract

The skip-lot sampling plan (SkSP) is employed in supply chains to decrease the amount of inspection required for submitted lots when they have demonstrated a succession of lots with excellent quality. As only some fractions of lots are examined, the cost of inspection is reduced. With the current abundance of high-yield products, however, the majority of SkSP schemes have been utilized for attributes testing, which does not fully reveal the SkSP’s economic advantages. Thus, on the basis of the process capability index Cpk, the variables SkSP with single sampling as a reference plan (Cpk-SkSP-2) was developed. With management of the lot’s quality and tolerable risks agreeable to both the supplier and the buyer, the Cpk-SkSP-2 were incorporated with acceptance probabilities (rather than asymptotic approximations), which yielded the exact sampling distribution of the Cpk estimator at the specified quality standards. Furthermore, the equilibrium probability for the acceptance of Cpk-SkSP-2 was derived from a Markov chain technique. These treatments enable minimization of the average number of samples required to render more reliable and optimal plan parameters for the inspection of products with a low fraction of defectives. The results are compared with the variables Cpk-based single sampling plans. Finally, a graphical user interface was built on the basis of our proposed Cpk-SkSP-2 procedures and methodologies to facilitate data input, plan selection, criteria computation, and decision-making in practice.

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Acknowledgements

This work was partially supported by the Ministry of Science and Technology, Taiwan under Grant Nos. MOST 103-2221-E-007-103-MY3

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Authors and Affiliations

  1. Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan

    Chien-Wei Wu & Pei-An Wang

  2. Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan

    Ming-Hung Shu

  3. Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung, Taiwan

    Bi-Min Hsu

  4. Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Kaohsiung, Taiwan

    Ming-Hung Shu

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  1. Chien-Wei Wu
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  2. Ming-Hung Shu
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  3. Pei-An Wang
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Correspondence to Chien-Wei Wu.

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Wu, CW., Shu, MH., Wang, PA. et al. Variables skip-lot sampling plans on the basis of process capability index for products with a low fraction of defectives. Comput Stat 36, 1391–1413 (2021). https://doi.org/10.1007/s00180-020-01049-0

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  • DOI: https://doi.org/10.1007/s00180-020-01049-0

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