Mixed Moving Average-Cumulative Sum Control Chart for Monitoring Parameter Change

Nongnuch Saengsura,Saowanit Sukparungsee,Yupaporn Areepong

doi:10.32604/iasc.2022.019997

Abstract

In this research, we propose the new mixed control chart called the mixed Moving Average-Cumulative Sum (MA-CUSUM) control chart used for monitoring parameter changes in asymmetrical and symmetrical processes. Its efficiency was compared with that of the Shewhart, Cumulative Sum (CUSUM), Moving Average (MA), mixed Cumulative Sum-Moving Average (CUSUM-MA) and mixed Moving Average-Cumulative Sum (MA-CUSUM) control charts by using their average run lengths (ARLs), the standard deviation of the run length (SDRL), and median run length (MRL) via the Monte Carlo simulation (MC). The simulation results show that the MA-CUSUM control chart was more efficient than the other control charts for small-to-moderate parameter changes for all distributions tested. To compare their applicability to real-world situations, the control charts were applied to data for the River Nile flow from 1871–1930 and mine explosions in the UK from 1875–1951. It was found that the MA-CUSUM control chart could more quickly detect parameter changes than the other control charts.

Highlights

Controlling product quality is essential in the manufacturing industry, and themost popular and widely used tool is the statistical process control chart
In this research, we propose the new mixed control chart called the mixed Moving Average-Cumulative Sum (MA-CUSUM) control chart used for monitoring parameter changes in asymmetrical and symmetrical processes
When l 1⁄4 0, r2 1⁄4 1, the CUSUM control chart obtained K1 1⁄4 0:3866 for w 1⁄4 5; h 1⁄4 5; L 1⁄4 3 and ARL1, standard deviation of the run length (SDRL), and median run length (MRL) values were lower than the others at parameter change levels -0.05, -0.10, -0.25, -0.50, -2.00, -3.00, -4.00, 0.05, 0.10, 0.25, 0.50, 2.00, 3.00, and 4.00

Summary

Introduction

Controlling product quality is essential in the manufacturing industry, and themost popular and widely used tool is the statistical process control chart. Page [2] presented the cumulative sum (CUSUM) control chart using weighted historical data that is effective at detecting smallto-meoderate changes in process parameters. Roberts [3] proposed the exponentially weighted moving average (EWMA) control chart in which historical data are weighted, which is effective at detecting small-to-moderate changes in process parameters. Taboran et al [8] proposed the new control chart: MA-EWMA to detect a change in process mean underlying asymmetric and symmetric processes, and compare the efficiency in monitoring the change with Shewhart, EWMA and MA control charts at the parameter change levels. Sukparungsee et al [10] proposed the mixed EWMAMA control chart to detect changes in the mean of processes with underlying symmetric and asymmetric distributions; the results of performance comparison showed that the mixed EWMA-MA control chart performed better and detected process mean shifts more quickly than the individual Shewhart, MA, and EWMA control charts. We compared the efficacies of the control charts by applying them to real data for the River Nile flow and mine explosions in the UK from 1875-1951

The CUSUM Control Chart

The MA Control Chart

Performance Measurement Evaluation

Simulation Study Results

Conclusions and Discussions