Construction of fuzzy X¯−S control chart using trapezoidal fuzzy number with unbalanced data

ABSTRACT

Statistical quality control is the most useful tool to monitor the process, whether it is the control or not under certain conditions, quality control technique for monitoring the production process through balanced data. In some cases, there are some uncertainties, and unbalanced data are presented. In these circumstances, obtaining the control limit is ineffective for the control charts. This paper deals with obtaining a fuzzy $\overline{X}-S$ chart by using trapezoidal fuzzy number (TpFN). The unbalanced TpFN information for each sample is converted and deals with the fuzzy $\overline{X}-S$ chart. The proposed technique is considered how to deal with the unbalanced control limits. Instead, we conducted a fuzzy process capability performance to measure the process performance. Lastly, we illustrate with an example to show the efficiency of the proposed fuzzy chart for uncertain information.

KEYWORDS:

• Trapezoidal fuzzy number
• fuzzy $\overline{X}-S$ chart
• fuzzy process capability
• unbalanced information
• statistical quality control
• statistical process control

Disclosure statement

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