A control chart to monitor the process mean based on inspecting attributes using control limits of the traditional X-bar chart

ABSTRACT

This paper proposes a new control chart, denoted by ${\overline{X}}^{tn}$, for evaluating the stability of a process mean, which is based on attribute inspection. In the ${\overline{X}}^{tn}$ control chart, the mean of the quality characteristic of interest is controlled by a go-no-go gauge device that generates five categorizations. In equally-spaced times, samples of n items are collected, their categories are determined, and random values are generated according to a truncated normal distribution that corresponds to their categories. With these random values, the averages are estimated and the ${\overline{X}}^{tn}$ control charts are built. Extensive computational experiments shown that the newly introduced ${\overline{X}}^{tn}$ control charts perform similarly to the usual $\overline{X}$ control chart in terms of average run length, provided that the sample sizes are raised by approximately three additional sample units. Because the ${\overline{X}}^{tn}$ control charts use attributes, they can be considered a viable alternative to the traditional $\overline{X}$ control chart.

KEYWORDS:

• Quality
• $\overline{X}$ control chart
• attribute and variable control charts
• average run length

Acknowledgement

We would like to thank the editor and two referees for their detailed and insightful comments, which led to a much-improved manuscript.

Disclosure statement

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

ORCID

R. C. Quinino http://orcid.org/0000-0002-2178-1331

L. L. Ho http://orcid.org/0000-0001-9984-8711

F. R. B. Cruz http://orcid.org/0000-0001-5842-5544

L. F. Bessegato http://orcid.org/0000-0002-5004-6790

Additional information

Funding

This research has been partially funded by the Brazilian agencies CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico of the Ministry for Science and Technology), under grants #305515/2018-7 and #301994/2018-8 and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais), under grant #CEX-PPM-00564-17.