Mixed exponentially weighted moving average – double moving average control chart base on sign statistic and its applications

Weerawat Sudsutad; Yupaporn Areepong; Saowanit Sukparungsee; Weerawat Sudsutad; Yupaporn Areepong; Saowanit Sukparungsee

doi:10.3934/math.2026180

AIMS Mathematics

2026, Volume 11, Issue 2: 4479-4521. doi: 10.3934/math.2026180

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Mixed exponentially weighted moving average – double moving average control chart base on sign statistic and its applications

Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand

Received: 08 November 2025 Revised: 19 December 2025 Accepted: 09 January 2026 Published: 13 February 2026
MSC : 62G05, 62P10, 62P30

Control charts are proposed with the assumption that the process's quality parameter follows a normal distribution. However, in fact, the normality assumption is rarely applied in practice. Parametric charts have a greater false alarm rate and more incorrect out-of-control comparisons in non-normal scenarios. Because the actual distribution of the quality parameter at issue is unknown, nonparametric charts are a strong and useful tool for evaluating a technique. This work proposes a nonparametric mixed exponentially weighted moving average–double moving average chart based on sign statistics to monitor the change in the process's mean under symmetric and asymmetric distributions. The proposed techniques are notable for their efficiency in identifying modest and persistent shifts in the process's location that match the supplied smoothing parameter values. The efficacy of the proposed chart was established through Monte Carlo (MC) simulation utilizing an average run length (ARL), a median run length (MRL), and the standard deviation of run length (S-DRL). Additionally, the average extra quadratic loss (AEQL), performance comparison index (PCI), and relative mean index (RMI) are additional metrics of overall performance that are applied to assess the utility of control charts. The proposed chart is found to be more effective in detecting a small mean shift in the processes faster than alternative charts such as the Shewhart, exponentially weighted moving average (EWMA), moving average (MA), double moving average (DMA), mixed EMMA–MA (MEM), and mixed EWMA–DMA (MEDM) charts under different symmetrical and asymmetrical distributions. In addition, the proposed and existing charts have been applied to three real-life data-sets: (ⅰ) The die-casting hot chamber process used in manufacturing zinc alloy parts for the sanitary industry, (ⅱ) the survival times of a cluster of patients suffering from head and neck cancer disease who were treated with radiotherapy, and (ⅲ) the measurements of the outer diameter at the base of the stem of an exhaust valve bridge.
- nonparametric,
- control chart,
- exponentially weighted moving average,
- double moving average,
- sign,
- average run length
Citation: Weerawat Sudsutad, Yupaporn Areepong, Saowanit Sukparungsee. Mixed exponentially weighted moving average – double moving average control chart base on sign statistic and its applications[J]. AIMS Mathematics, 2026, 11(2): 4479-4521. doi: 10.3934/math.2026180

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Abstract

Control charts are proposed with the assumption that the process's quality parameter follows a normal distribution. However, in fact, the normality assumption is rarely applied in practice. Parametric charts have a greater false alarm rate and more incorrect out-of-control comparisons in non-normal scenarios. Because the actual distribution of the quality parameter at issue is unknown, nonparametric charts are a strong and useful tool for evaluating a technique. This work proposes a nonparametric mixed exponentially weighted moving average–double moving average chart based on sign statistics to monitor the change in the process's mean under symmetric and asymmetric distributions. The proposed techniques are notable for their efficiency in identifying modest and persistent shifts in the process's location that match the supplied smoothing parameter values. The efficacy of the proposed chart was established through Monte Carlo (MC) simulation utilizing an average run length (ARL), a median run length (MRL), and the standard deviation of run length (S-DRL). Additionally, the average extra quadratic loss (AEQL), performance comparison index (PCI), and relative mean index (RMI) are additional metrics of overall performance that are applied to assess the utility of control charts. The proposed chart is found to be more effective in detecting a small mean shift in the processes faster than alternative charts such as the Shewhart, exponentially weighted moving average (EWMA), moving average (MA), double moving average (DMA), mixed EMMA–MA (MEM), and mixed EWMA–DMA (MEDM) charts under different symmetrical and asymmetrical distributions. In addition, the proposed and existing charts have been applied to three real-life data-sets: (ⅰ) The die-casting hot chamber process used in manufacturing zinc alloy parts for the sanitary industry, (ⅱ) the survival times of a cluster of patients suffering from head and neck cancer disease who were treated with radiotherapy, and (ⅲ) the measurements of the outer diameter at the base of the stem of an exhaust valve bridge.

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