A new adaptive CUSUM control chart based on Hampel function to monitor location parameter

Abstract To identify small‐to‐moderate shifts (also known as outliers and anomalies) in the process parameters (location and/or dispersion), the classical cumulative sum (CUSUM) and exponential weighted moving average (EWMA) control charts are famous. The traditional CUSUM control chart is less capable to detect out‐of‐control signals of 1.0 standard deviation shifts. The advanced versions of the traditional CUSUM and EWMA control charts are ACUSUM (adaptive CUSUM) and AEWMA (adaptive EWMA) control charts, respectively. The aforementioned issue of the traditional CUSUM control chart can be addressed through the ACSUUM control chart. It also identifies various sizes of shifts in the process parameters. In order to efficiently identify and remove outliers and anomalies (i.e., shifts) from datasets, the score functions are typically used to establish ACUSUM control charts. The goal of the study is to propose a new ACUSUM control chart based on the Hampel (score) function and it is symbolized as control chart. Different sizes of shift in the process location parameter can be distinguished using the control chart. The primary novelty is the substitution of a proposed time‐varying parameter for the typical CUSUM control chart's prioritization of the process characteristic by appropriate weights. The proposed control chart's run length feature is obtained through the Monte Carlo simulation technique for zero‐state and steady‐states. For evaluating a single shift, performance measures like average run length (ARL), standard deviation of run length (RL), and different percentiles of run length are preferred. However, for evaluating a range of shifts, extra quadratic loss, relative average run length, and performance comparison index are used. Comparison based on performance measures shows the superiority of the proposed control chart against the classical CUSUM and EWMA, ACUSUM, AEWMA, mixed EWMA‐CUSUM, and mixed CUSUM‐EWMA control charts. Furthermore, the proposed control chart is also implemented with real‐life data which is taken from cost of medical insurance to demonstrate its competency in statistical process control field for quality engineers, practitioners, experts, and researchers.