A non-parametric CUSUM control chart for process distribution change detection and change type diagnosis

Abstract

Non-parametric control charts have been good alternatives to parametric control charts when little information is known about the type of process distribution or the value of parameters. Most approaches proposed by the current literature monitor either location or scale change in batch mode and their performance is discounted when monitoring distribution change in both location and scale simultaneously in a sequential pattern. This paper proposed a log-likelihood-ratio-based non-parametric cumulative sum (CUSUM) control chart to monitor arbitrary distribution change and diagnose the detailed change type simultaneously. By integrating the superiority of log-likelihood ratio test to detect any change of distribution and CUSUM chart to detect a small change, the proposed approach can detect small potential changes in location, scale and shape; and provide detailed information about change type when control chart gives a signal. Comparison results with many other non-parametric approaches were provided by numerical simulation and the results of an application case demonstrate the effectiveness of the proposed approach.

Keywords:

• log-likelihood ratio
• CUSUM
• change point detection
• change type diagnosis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper was supported in part by China Scholarship Fund [CSC No.201708430274]; Scientific Research Fund of Hunan Provincial Education Department [grant number16B208]; Humanities and Social Sciences Project of Hunan Province [grant number16YBX018].