On the sensitivity of robust control charts in monitoring contaminated data

Abstract

Shewhart chart is typically formed under normality assumptions. In reality, much data is contaminated with occasional outliers, which may diminish the Shewhart chart’s sensitivity. Hence, robust charts are introduced as outlier-resistant and robust against non-normality. This paper intends to study the robust monitoring of contaminated data using (i) median chart based on median absolute deviation (MAD), and (ii) trimmed mean chart based on winsorized standard deviation. These charts are compared with the conventional Shewhart mean ( ) X charts based on standard deviation and range. In general, through extensive simulations, the robust charts are quite comparable with the X charts for normal data of small sample size (n), but for large n, the median chart based on MAD is marginally preferred by all the benchmarks considered. However, when a process is contaminated, both robust charts outshine the X charts substantially in a series of investigations.

Keywords

• shewhart chart
• robust
• outlier
• contamination
• standard deviation