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

Mohammad Ahmad · Weihu Cheng · Ahteshamul Haq · Sayed Kifayat Shah

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Fuzzy Systems and Optimization

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 X¯−S chart by using trapezoidal fuzzy number (TpFN). The unbalanced TpFN information for each sample is converted and deals with the fuzzy 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.

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References

2002Process Capability Indices—A Review, 1992–2000 1997Introduction to Statistical Quality Control 2010A bibliography of the literature on process capability indices: 2000–2009 2006An alternative approach to fuzzy control charts: Direct fuzzy approach 2008Development of fuzzy X¯∼-R∼ and X¯∼-S∼ control charts using α-cuts 2014Fuzzy exponentially weighted moving average control chart for univariate data with a real case application 2011Process capability analyses with fuzzy parameters 2009Fuzzy multivariate exponentially weighted moving average control chart

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