Construction of¯X − R control charts using Beta distribution for triangular fuzzy quality

The primary objective of statistical quality control is to ensure that products or services meet predetermined standards while minimizing variation and instability in processes. Control charts are indispensable tools in quality control, playing a crucial role in enhancing and improving process quality. Given their significance, incorporating fuzzy quality into control charts introduces flexibility into product quality assessment. In this paper, we design mean (¯ X) and range (R) control charts based on fuzzy quality, as opposed to traditional crisp or precise quality. We construct quantile-based control charts for the degree of membership of observations to triangular fuzzy quality using parameter estimation in the beta distribution. Specifically, we propose two novel methods for constructing¯ X and R control charts, namely, the method of moments and maximum likelihood estimation, both based on triangular fuzzy quality.

Keywords:

Quantile-based control chart , fuzzy quality , Beta distribution , Maximum likelihood estimation , Method of moments estimation