False Discovery Rate-Adjusted Charting Schemes for Multistage Process Monitoring and Fault Identification

Abstract

Most statistical process control research focuses on single-stage processes. This article considers the problem of multistage process monitoring and fault identification. This problem is formulated as a multiple hypotheses testing problem; however, as the number of stages increases, the detection power of multiple hypotheses testing methods that seek to control the type I error rate decreases dramatically. To maintain the detection power, we use a false discovery rate (FDR) control approach, which is widely used in microarray research. Two multistage process monitoring and fault identification schemes—an FDR-adjusted Shewhart chart and an FDR-adjusted cumulative sum (CUSUM) chart—are established. To apply the FDR approach, the distribution of the CUSUM statistics are obtained based on Markov chain theory and Brownian motion with drift models. The detection and fault identification power of the new schemes are evaluated by the Monte Carlo method. The results indicate that the novel FDR-adjusted approaches are better at identifying the faulty stage than the conventional type I error rate control approach, especially when multiple out-of-control stages are present.

Keywords:  :

• Distribution of the CUSUM statistic
• False discovery rate
• Multistage process
• State-space model