Performance of new nonparametric Tukey modified exponentially weighted moving average—Moving average control chart

Abstract

Control charts are an amazing and essential statistical process control (SPC) instrument that is commonly used in monitoring systems to detect a specific defect in the procedure. The mixed Tukey modified exponentially weighted moving average - moving average control chart (MMEM-TCC) with motivation detection ability for fewer shifts in the process mean under symmetric and non-symmetric distributions is proposed in this paper. Average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) were used as efficiency criteria in the Monte Carlo simulation, and their efficiency was compared to existing control charts. Furthermore, the expected ARL (EARL) is a method for evaluating the performance of control charts beyond a specific range of shift sizes. The distinguishing feature of the proposed chart is that it performs efficiently in detecting small to moderate shifts. There are applications for PM 2.5 and PM 10 data that demonstrate the performance of the proposed chart.

Beyond the EWMA chart: Critiquing hybrid approaches

“…Talordphop et al 12 . suggested two variants of the EWMA charts, the mEWMA–EWMA and EWMA–mEWMA charts.…”

“…Both the mEWMA–EWMA and EWMA–mEWMA charts are designed to trigger an out‐of‐control state when $$|H_{t}|>h_{5}$$ or $$|I_{t}|>h_{6}$$ to signal a change in the in‐control mean of $$Z_{t}$$ at time $$t$$, respectively. For more details, we refer to Talordphop et al 12 …”

“…Moreover, following Khan et al, 5 Talordphop et al 11 proposed two mixed variants of the EWMA charts: (1) mEWMA chart based on the MA statistic (mEWMA-MA), and (2) MA chart based on the mEWMA statistic (MA-mEWMA), for the process mean. In addition, Talordphop et al 12 suggested two more variants of the EWMA charts for the process mean: (1) EWMA statistic-based mEWMA chart (mEWMA-EWMA), and (2) mEWMA statistic-based EWMA chart (EWMA-mEWMA).…”

“…The mEWMA-EWMA and EWMA-mEWMA chart Talordphop et al12 suggested two variants of the EWMA charts, the mEWMA-EWMA and EWMA-mEWMA charts. The mEWMA-EWMA chart is basically an mEWMA chart with the EWMA statistic as an input.…”

Max-mixed EWMA control chart for joint monitoring of mean and variance: an application to yogurt packing process

“…It is clear from this comparison that the proposed chart outperforms the current alternatives. The Modified Exponentially Weighted Moving Average—Moving Average Control Chart (MMEM) was proposed by 12 to monitor changes in the process mean. The proposed chart outperformed alternative control charts through both simulated and practical examination.…”