Enhanced CUSUM and dual CUSUM mean charts

Abstract

The CUSUM (C) and dual C (DC) charts are well-known because of their sensitive nature against small-to-moderate shifts that occur in the process parameter(s). In this study, we propose new auxiliary information based (AIB) control charts for monitoring the process mean, which include Brownian motion-based C (BC), new BC (NBC), NBC with Crosier C (NBCC), dual NBC (DNBC) and dual NBCC (DNBCC) charts. In addition, fast initial response feature is also added to the proposed charts. We use Monte Carlo simulations to compute the run length properties of the control charts. Based on detailed run length comparisons, it is found that the proposed AIB charts are uniformly better than the existing AIB charts in terms of expected weighted and relative average run length benchmarks. An important concern all around the world is the quality and safety of drinking water. Several water quality tests are available that provide required information about the health of the waterway. Here, a water quality test dataset is taken on two variables, namely pH and total solids, and the proposed AIB charts are used to monitor the mean level of pH in the water.

KEYWORDS:

• Auxiliary information
• average run length
• CUSUM
• dual CUSUM
• Monte Carlo simulation
• process mean
• statistical process control

Acknowledgment

The authors are thankful to the anonymous reviewer for providing useful comments that led to an improved version of the article.