Profile monitoring using synthetic T² control chart

Abstract

In this paper, we propose synthetic $T^2$ chart for monitoring different parameters including Slope, Intercept and Error variance for simple and multiple linear regression profiles in Phase II. The construction and optimal design of the proposed synthetic $T^2$ chart are discussed in detail. The steady-state performance of the proposed chart is evaluated by the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) and is compared with the existing charts in the literature for monitoring simple and multiple linear profiles. It turns out that the proposed synthetic $T^2$ chart performs uniformly better than the traditional $T^2$ chart in detecting different kinds of shifts in the parameters of the simple and multiple linear profiles under steady-state run length performance. An example with a real data set is also presented to explain the implementation of the proposed chart.

Keywords:

• Average run length
• Control chart
• Intercept
• Linear regression profiles
• Slope

Acknowledgements

The authors thank the editor in chief and the two anonymous referees for their many helpful comments that have resulted in significant improvements to the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).