A novel approach to monitor simple linear profiles using individual observations

Abstract

In some quality control applications, quality of a product or process may be characterized effectively by a functional relationship between one or more variables that is typically referred to as a profile. In this paper, we propose four control charts, namely the maximum CUSUM (MaxCUSUM), maximum Crosier CUSUM (MaxCCUSUM), maximum EWMA (MaxEWMA) and maximum double EWMA (MaxDEWMA) charts, for monitoring the parameters of a Phase II simple linear profile using the individual observations. In addition, the sensitivities of these control charts are also enhanced with the variable sampling interval feature. The Monte Carlo simulation method is used to compute the zero-state and steady-state run length characteristics of the proposed charts. The run length comparisons reveal that the MaxCCUSUM (MaxDEWMA) chart is slightly more sensitive than the MaxCUSUM (MaxEWMA) chart. A real dataset is also considered to support the theory.

Keywords:

• Average run length
• Control chart
• MaxCCUSUM
• MaxCUSUM
• MaxEWMA
• MaxDEWMA
• Monte Carlo simulation
• Profile monitoring
• Statistical process control
• Zero-state and steady-state

Acknowledgments

The authors are thankful to three anonymous reviewers for providing useful comments that led to an improved version of the article.