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Monitoring imprecise fraction of nonconforming items using p control charts

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  • Ming-Hung Shu
  • Hsien-Chung Wu

Abstract

The quality characteristics, which are known as attributes, cannot be conveniently and numerically represented. Generally, the attribute data can be regarded as the fuzzy data, which are ubiquitous in the manufacturing process and cannot be measured precisely and often be collected by visual inspection. In this paper, we construct a p control chart for monitoring the fraction of nonconforming items in the process in which fuzzy sample data are collected from the manufacturing process. The resolution identity - a well-known theorem in the fuzzy set theory - is invoked to construct the control limits of fuzzy-p control charts using fuzzy data. In order to determine whether the plotted imprecise fraction of nonconforming items is within the fuzzy lower and upper control limits, we also propose a ranking method for a set of fuzzy numbers. Using the fuzzy-p control charts and the proposed acceptability function to classify the manufacturing process allows the decision-maker to make linguistic decisions such as rather in control or rather out of control. A practical example is provided to describe the applicability of the fuzzy set theory to a conventional p control chart.

Suggested Citation

  • Ming-Hung Shu & Hsien-Chung Wu, 2010. "Monitoring imprecise fraction of nonconforming items using p control charts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1283-1297.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:8:p:1283-1297
    DOI: 10.1080/02664760903030205
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    Cited by:

    1. Su-Fen Yang & Li-Pang Chen & Cheng-Kuan Lin, 2023. "Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable," Sustainability, MDPI, vol. 15(5), pages 1-19, February.

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