Revisiting the np(x) Control Chart: Performance Insights and the Impact of Parameter Estimation

Music City Center 

The np(x) control chart, introduced by Wu et al. (2009), was designed to monitor the mean of a continuous variable using attribute inspection. While this approach offers advantages such as simplicity and cost-effectiveness, our re-examination reveals inconsistencies in prior performance assessments and provides new insights. Specifically, we demonstrate that for a two-sided np(x) chart to outperform the traditional Xbar chart, the required sample size must be significantly larger than previously recommended. Additionally, in practice, control charts are typically designed using estimated parameters, yet prior studies on the np(x) chart assume known parameters. We extend the analysis to this more realistic setting, showing that parameter estimation inflates the in-control average run length (ARL0), leading to a higher-than-expected false alarm rate. Through theoretical derivations and numerical studies, we identify conditions where the np(x) chart remains competitive and propose strategies to mitigate estimation effects. These findings refine our understanding of attribute-based control charts for mean monitoring and offer practical guidance for their implementation.

Parameter Estimation

False Alarm Rate

Average Run Length

Attribute control charts

np(x) chart Control Chart 

Quality and Productivity Section