The use of npx$np_{x}$‐type attribute charts to monitor the variance

Abstract

First, the 𝑛𝑝 𝑥 -type attribute control charts have been proposed to monitor the process mean. The main contribution of this paper is to show the good performances of the "pure 𝑛𝑝 𝑥 " (shortly 𝑛𝑝 𝜎 2 𝑥 ) and "improved 𝑛𝑝 𝑥 " (shortly 𝑛𝑝 𝜎 2 𝑥(𝐼) ) attribute charts to monitor the variance. The results confirmed that they are also good alternatives to 𝑆 2 control chart. To have an equal performance (in terms of speed to detect abnormal cases), the sample size needed for these charts is slightly higher than those practiced for an 𝑆 2 control chart. This is an advantage since an attribute inspection is faster and cheaper as no measurements on the examined units are taken (mainly if we are dealing with destructive experiments). A numerical example illustrates our proposal.

An approach for improvements on the attribute npx$np_x$ control chart

“…Silva et al 20 proposed the application of a scheme to achieve improvements for the attribute 𝑛𝑝 𝑥 control chart in monitoring the process mean, extending posteriorly its use to monitor the variance. 21 Such scheme provides a significant reduction in terms of 𝐴𝑅𝐿 1 . It consists of the use of a same sequence in the selection of the sample sizes to be inspected (𝑛 𝑎 , 𝑛 𝑏 ) during the execution of the process monitoring, simplifying the decision-making, because it is a predetermined fixed sequence, especially when the results signal an in control condition.…”

“…Silva et al 20 . proposed the application of a scheme to achieve improvements for the attribute $$np_x$$ control chart in monitoring the process mean, extending posteriorly its use to monitor the variance 21 . Such scheme provides a significant reduction in terms of $$ARL_1$$.…”