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

Abstract Number:

1918 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Felipe Schoemer Jardim (1), Mariana Oliveira (2), Marcela Machado (2), Subhabrata Chakraborti (3)

Institutions:

(1) Fluminense Federal University (UFF), N/A, (2) São Paulo State University (UNESP), N/A, (3) The University of Alabama, N/A

Co-Author(s):

Mariana Oliveira  
São Paulo State University (UNESP)
Marcela Machado  
São Paulo State University (UNESP)
Subhabrata Chakraborti  
The University of Alabama

First Author:

Felipe Schoemer Jardim  
Fluminense Federal University (UFF)

Presenting Author:

Felipe Schoemer Jardim  
Fluminense Federal University (UFF)

Abstract Text:

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.

Keywords:

Parameter Estimation|False Alarm Rate|Average Run Length|Attribute control charts|np(x) chart Control Chart|

Sponsors:

Quality and Productivity Section

Tracks:

Statistical Process Control and Quality Assurance

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