On designing a new control chart for Rayleigh distributed processes with an application to monitor glass fiber strength

Abstract

In this study, a Shewhart type control chart, namely $V_R$ chart, has been proposed to monitor a process that follows Rayleigh distribution. The proposed $V_R$ chart is implemented to monitor the single scale parameter of the Rayleigh distributed process. We have studied the proposed chart under two type of control limits namely probability and $L$-sigma limits. The performance of the proposed chart has been assessed by using power function. In addition, we have investigated run length properties including average run length (ARL), standard deviation of run length (SDRL) and median run length (MDRL). The analysis of run length profile reveals that the proposed V_R chart outperforms the existing charts including the traditional Shewhart control chart and V control charts under Rayleigh distribution. The construction process for the newly proposed chart has been demonstrated using a simulated data. Finally, a real application of the proposed $V_R$ chart, along with the existing $V$ chart, is presented that evaluates the strength of glass fiber in a manufacturing process.

Keywords:

• Control chart
• Gamma distribution
• Maximum likelihood estimation
• Rayleigh distribution
• Run length

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05; 60K99; 62E10; 62E15; 62P30; 62Q05; 97K50; 97K80

Acknowledgments

The first and last authors gratefully acknowledged Department of Statistics, Faculty of Science, Bangabandhu Sheikh Mujibur Rahman Science & Technology University where the study has been primarily conducted.

Additional information

Funding

M. Pear Hossain is also thankful to the BSMRSTU authority for providing research grant no 5921.