Nonparametric Adaptive CUSUM Chart for Detecting Arbitrary Distributional Changes

TL;DR

This paper introduces a new nonparametric adaptive CUSUM control chart that detects arbitrary distributional changes efficiently without tuning parameters, suitable for small reference data, and includes diagnostics for identifying change types.

Contribution

The paper presents a novel nonparametric adaptive CUSUM chart that is parameter-free, computationally efficient, self-starting, and capable of diagnosing the type of distributional change.

Findings

Performs well across various settings in simulations and real data.

Outperforms existing nonparametric control charts.

Does not require large reference data or tuning parameters.

Abstract

Nonparametric control charts that can detect arbitrary distributional changes are highly desirable due to their flexibility to adapt to different distributional assumptions and distributional changes. However, most of such control charts in the literature either involve some tuning parameter, which needs to be pre-specified, or involve intensive computation. In this paper, we propose a new nonparametric adaptive CUSUM chart for detecting arbitrary distributional changes. The proposed control chart does not depend on any tuning parameter and is efficient in computation. Its self-starting nature makes the proposed control chart applicable to situations where no sufficiently large reference data are available. Our proposed control chart also has a built-in post-signal diagnostics function that can identify what kind of distributional changes have occurred after an alarm. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favorably with existing nonparametric control charts.