An adaptive EWMA control chart based on Hampel function to monitor the process location parameter.

The classical memory Exponential Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts (CCs) are important to detect small‐to‐moderate sizes of shift in the process location and/or dispersion parameters. To make the memory control chart (CC) more efficient for broad range of shift, the score functions in particular Huber and Bi‐square functions are incorporated in the classical memory CCs. These score functions help to formulate the parameters of memory CCs and are called Adaptive EWMA (AEWMA) and Adaptive CUSUM (ACUSUM). The AEWMA and ACUSUM are capable to handle various sizes (i.e., small, moderate, and large) of shift. The aim of this study is to utilize Hampel function as the alternative of the mentioned score functions, and propose a new AEWMA CC, symbolized as AEWMAHample. To develop the proposed AEWMAHample CC, the standard EWMA statistic and Hampel function are incorporated in the classical EWMA CC structure. The proposed AEWMAHample CC is also efficient to handle certain sizes of shift in the process location parameter. Performance evaluation procedures, like average run length is considered for a particular shift. Similarly, the performance comparison index, relative average run length, and extra quadratic loss function are estimated over a range of shift. All these performance measures are calculated from run length (RL) characteristic of the proposed control chart. An algorithm in MATLAB is developed based on Monte Carlo simulation procedure to generate the RLs. Some existing control charts including EWMA, CUSUM, MEC, MCE, ACUSUMc(1)${\rm{ACUSUM}}_{\rm{c}}^{(1)}$, ACUSUMc(2)${\rm{ACUSUM}}_{\rm{c}}^{(2)}$, IACCUSUM, AEWMA∅hu${\rm{AEWMA}}_{{\emptyset }_{{\rm{hu}}}}$, and AEWMA∅bs${\rm{AEWMA}}_{{\emptyset }_{{\rm{bs}}}}$ are taken for comparison reason. For specific sizes of shift, the proposed AEWMAHample CC reveals the superiority. Besides, to address the practical significance for practitioners and quality engineers, the real‐life and simulated data examples are considered. [ABSTRACT FROM AUTHOR]