scholarly journals The performance of a modified EWMA control chart for monitoring autocorrelated PM2.5 and carbon monoxide air pollution data

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10467
Author(s):  
Yadpirun Supharakonsakun ◽  
Yupaporn Areepong ◽  
Saowanit Sukparungsee
Keyword(s):  
Air Pollution ◽  
Carbon Monoxide ◽  
Control Chart ◽  
Negative Impact ◽  
Average Run Length ◽  
Moving Average ◽  
Integral Equation Method ◽  
Liquid Droplets ◽  
Ewma Control Chart ◽  
Weighted Moving Average

PM2.5 (particulate matter less than or equal to 2.5 micron) is found in the air and comprises dust, dirt, soot, smoke, and liquid droplets. PM2.5 and carbon monoxide emissions can have a negative impact on humans and animals throughout the world. In this paper, we present the performance of a modified exponentially weighted moving average (modified EWMA) control chart to detect small changes when the observations are autocorrelated with exponential white noise through the average run length evaluated (ARLs) by explicit formulas. The accuracy of the solution was verified with a numerical integral equation method. The efficacy of the modified EWMA control chart to monitor PM2.5 and carbon monoxide air pollution data and compare its performance with the standard EWMA control chart. The results suggest that the modified EWMA control chart is far superior to the standard one.

An EWMA control chart based on the Wilcoxon rank-sum statistic using repetitive sampling

2018 ◽  
Vol 35 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Jean-Claude Malela-Majika ◽  
Olatunde Adebayo Adeoti ◽  
Eeva Rapoo
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Location Parameter ◽  
Process Mean ◽  
Content Type ◽  
Underlying Process ◽  
Run Length ◽  
Design And Implementation ◽  
Ewma Control Chart

Purpose The purpose of this paper is to develop an exponentially weighted moving average (EWMA) control chart based on the Wilcoxon rank-sum (WRS) statistic using repetitive sampling to improve the sensitivity of the EWMA control chart to process mean shifts regardless of the prior knowledge of the underlying process distribution. Design/methodology/approach The proposed chart is developed without any distributional assumption of the underlying quality process for monitoring the location parameter. The authors developed formulae as well as algorithms to facilitate the design and implementation of the proposed chart. The performance of the proposed chart is investigated in terms of the average run-length, standard deviation of the run-length (RL), average sample size and percentiles of the RL distribution. Numerical examples are given as illustration of the design and implementation of the proposed chart. Findings The proposed control chart presents very attractive RL properties and outperforms the existing nonparametric EWMA control chart based on the WRS in the detection of the mean process shifts in many situations. However, the performance of the proposed chart relatively deteriorates for small phase I sample sizes. Originality/value This study develops a new control chart for monitoring the process mean using a two-sample test regardless of the nature of the underlying process distribution. The proposed control chart does not require any assumption on the type (or nature) of the process distribution. It requires a small number of subgroups in order to reach stability in the phase II performance.

scholarly journals The Expected Average Run Length of the EWMA Median Chart with Estimated Process Parameters

2020 ◽  
Vol 49 (3) ◽  
pp. 19-24
Author(s):  
Huay Woon You ◽  
Michael Khoo Boon Chong ◽  
Chong Zhi Lin ◽  
Teoh Wei Lin
Keyword(s):  
Phase I ◽  
Control Chart ◽  
Process Parameters ◽  
Average Run Length ◽  
Moving Average ◽  
Background Knowledge ◽  
Exponentially Weighted Moving Average ◽  
Control Phase ◽  
Run Length ◽  
Weighted Moving Average

The performance of a control chart is commonly investigated based on the assumption of known process parameters. Nevertheless, in most manufacturing and service applications, the process parameters are usually unknown to practitioners. Hence, they are estimated from an in-control Phase-I samples. As such, the performance of the control chart with estimated process parameters will behave differently from the corresponding chart with known process parameters. To study this issue, the exponentially weighted moving average (EWMA) median chart is examined in this article. The EWMA median chart is traditionally investigated based on the average run length (ARL). The limitation of the ARL is that it requires practitioners to specify the shift size in advance. This phenomenon is not ideal for practitioners who do not have background knowledge of the process. In view of this, the EWMA median chart with known and estimated process parameters is studied based on the ARL and expected average run length (EARL). The results indicate that as long as the particular shift size is within the range of shifts, the performance of the chart is almost the same, for the EWMA median chart with known and estimated process parameters.

Design of a Variable Sampling Interval EWMA Median Control Chart

2019 ◽  
Vol 26 (05) ◽  
pp. 1950021 ◽  
Author(s):  
Kim Phuc Tran ◽  
Philippe Castagliola ◽  
Thi Hien Nguyen ◽  
Anne Cuzol
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Food Production ◽  
Average Run Length ◽  
Moving Average ◽  
Sampling Interval ◽  
Performance Comparison ◽  
Variable Sampling Interval ◽  
Variable Sampling ◽  
Weighted Moving Average

In the literature, median type control charts have been widely investigated as easy and efficient means to monitor the process mean when observations are from a normal distribution. In this work, a Variable Sampling Interval (VSI) Exponentially Weighted Moving Average (EWMA) median control chart is proposed and studied. The Markov chains are used to calculate the average run length to signal (ARL). A performance comparison with the original EWMA median control chart is made. The numerical results show that the proposed chart is considerably more effective as it is faster in detecting process shifts. Finally, the implementation of the proposed chart is illustrated with an example in food production process.

Demerit-GWMA Control Chart for Demerit Statistics

2010 ◽  
Vol 156-157 ◽  
pp. 413-421
Author(s):  
Hae Woon Kang ◽  
Chang Wook Kang ◽  
Jae Won Baik ◽  
Sung Ho Nam
Keyword(s):  
Control Chart ◽  
Mobile Phones ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Process Mean ◽  
Average Technique ◽  
Complex Products ◽  
Ewma Control Chart ◽  
Weighted Moving Average ◽  
Exponentially Weighted

A classical Demerit control chart is used to monitor the process through which various types of defects in complex products, such as automobiles, computers, mobile phones, etc. are found in general. As a technique for rapidly detecting small shifts of the process mean in the control chart, the EWMA(exponentially weighted moving average) technique is very effective. This study suggested the Demerit-GWMA control chart, combining the GWMA(generally weighted moving average) technique, which shows better performance than EWMA technique in detecting small shifts of process mean, into the classical Demerit control chart, and evaluated its performance. Through the evaluation of its performance, it was found that the Demerit-GWMA control chart is more sensitive than both the classical Demerit control chart and the Demerit-EWMA control chart in detecting small shifts of process mean.

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