A Fuzzy Bivariate Poisson Control Chart

Abstract

In the present paper, we develop a fuzzy bivariate Poisson (FBP) control chart based on a fuzzy c chart. The FBP chart is used to monitor the sum of the nonconformities of each quality characteristic. There are two contributions of this work. First, we propose a new fuzzy parameter estimation to create a triangular fuzzy number (TFN). Second, our control chart is flexible, because we involve the α c u t to measure the level of tightness of inspection. Furthermore, the statistic of FBP is being able to visualise the monitoring process in a graphical form. In addition, the simulation study indicates that the performance of our proposed chart, based on average run length (ARL), is more sensitive than the performance of a conventional bivariate Poisson (BP) chart. Moreover, an illustration example shows that the FBP chart has relatively more sensitive performance compared to the conventional BP chart.

Keywords

• control chart
• fuzzy bivariate Poisson
• TFN
• <i>α^cut</i>
• average run length