Using VSI Loss Control Charts to Monitor a Process with Incorrect Adjustment

Abstract

The article considers the optimum variables control scheme for a process with incorrect adjustment. Incorrect adjustment of a process may result in shifts in process mean and/or variance, ultimately affecting the quality of products and creating a loss. For the process with incorrect adjustment, we construct the variable sampling interval (VSI) and Z _{S ²} control charts to monitor the shifts in the process mean and variance and with minimum loss. The minimum loss variable sampling interval control charts is measured by the average loss per unit time derived by a Markov chain approach. An example is given to show the application and the performance of the proposed control charts. Furthermore, the comparison of the performance of the VSI loss control charts and the fixed sampling interval (FSI) loss control charts suggested that the VSI charts outperformed that of FSI charts.

Keywords:

• Control charts
• Fixed sampling interval
• Incorrect adjustment
• Loss function
• Markov chain
• Variable sampling interval

Mathematics Subject Classification:

• 62P30
• 62P99

Acknowledgments

Support for this research was provided in part by the National Science Council of the Republic of China, grant No. NSC 94-2118-M-004-003, and Center for Service Innovation, National Chengchi University, Taiwan.