Auxiliary-information-based efficient variability control charts for Phase I of SPC

Abstract

The inclusion of correlated auxiliary variables into the monitoring scheme of quality characteristic of interest has gained notable attention in recent statistical process control (SPC) literature. Several authors have investigated the use of a correlated auxiliary variable for efficient monitoring of variability in Phase II of SPC. This phase is generally used to detect any shifts in the expected behavior of the process parameters which are often estimated from the historical in-control process in Phase I. However, no study has investigated the performance of auxiliary-based variability charts in Phase I of SPC. Here, we propose auxiliary-based dispersion control charts in Phase I of SPC. The auxiliary information is considered in the forms of regression, ratio, exponential, and power-ratio forms. The performance of the variability charts is evaluated and compared using probability to signal as a performance measure. An illustrative example is also provided to show the application of the charts. This study will provide practitioners with appropriate recommendations on the choice of dispersion charts for Phase I analysis.