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Zaagan AA, Khan I, Alzahrani ARR, Ahmad B. Parameter free AEWMA control chart for dispersion in semiconductor manufacturing. Sci Rep 2024; 14:10512. [PMID: 38714824 PMCID: PMC11076580 DOI: 10.1038/s41598-024-61408-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 05/06/2024] [Indexed: 05/10/2024] Open
Abstract
The study presents a new parameter free adaptive exponentially weighted moving average (AEWMA) control chart tailored for monitoring process dispersion, utilizing an adaptive approach for determining the smoothing constant. This chart is crafted to adeptly detect shifts within anticipated ranges in process dispersion by dynamically computing the smoothing constant. To assess its effectiveness, the chart's performance is measured through concise run-length profiles generated from Monte Carlo simulations. A notable aspect is the incorporation of an unbiased estimator in computing the smoothing constant through the suggested function, thereby improving the chart's capability to identify different levels of increasing and decreasing shifts in process dispersion. The comparison with an established adaptive EWMA-S2 dispersion chart highlights the considerable efficiency of the proposed chart in addressing diverse magnitudes of process dispersion shifts. Additionally, the study includes an application to a real-life dataset, showcasing the practicality and user-friendly nature of the proposed chart in real-world situations.
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Affiliation(s)
- Abdullah A Zaagan
- Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, 45142, Jazan, Kingdom of Saudi Arabia
| | - Imad Khan
- Department of Statistics, Abdul Wali Khan University Mardan, Mardan, 23200, Pakistan
| | - Ali Rashash R Alzahrani
- Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia
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Haridy S, Alamassi B, Maged A, Shamsuzzaman M, Al Owad A, Bashir H. Economic statistical model of the np chart for monitoring defectives. Sci Rep 2023; 13:13179. [PMID: 37580471 PMCID: PMC10425373 DOI: 10.1038/s41598-023-40151-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 08/05/2023] [Indexed: 08/16/2023] Open
Abstract
When monitoring manufacturing processes, managing an attribute quality characteristic is easier and faster than a variable quality characteristic. Yet, the economic-statistical design of attribute control charts has attracted much less attention than variable control charts in the literature. This study develops an algorithm for optimizing the economic-statistical performance of the np chart for monitoring defectives, based on Duncan's economic model. This algorithm has the merit of the economic model to minimize expected total cost, and the benefit of the statistical design to enhance the effectiveness of detecting increasing shifts in defectives. The effectiveness of the developed np chart is investigated under different operational scenarios. The results affirm a considerable superiority of the proposed np chart over the traditional np chart. Real-life data are used to demonstrate the applicability of the proposed np scheme, in comparison to the traditional np chart.
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Affiliation(s)
- Salah Haridy
- Department of Industrial Engineering and Engineering Management, College of Engineering, University of Sharjah, Sharjah, UAE.
- Benha Faculty of Engineering, Benha University, Benha, Egypt.
| | - Batool Alamassi
- Department of Industrial Engineering and Engineering Management, College of Engineering, University of Sharjah, Sharjah, UAE
| | - Ahmed Maged
- Benha Faculty of Engineering, Benha University, Benha, Egypt
- Department of Advanced Design and Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong
| | - Mohammad Shamsuzzaman
- Department of Industrial Engineering and Engineering Management, College of Engineering, University of Sharjah, Sharjah, UAE
| | - Ali Al Owad
- Department of Industrial Engineering, Faculty of Engineering, Jazan University, Jazan, Saudi Arabia
| | - Hamdi Bashir
- Department of Industrial Engineering and Engineering Management, College of Engineering, University of Sharjah, Sharjah, UAE
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Chen JH, Lu SL, Liao CT. An enhanced sum of squares generally weighted moving average chart based on auxiliary information for process monitoring. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2098498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Jen-Hsiang Chen
- Department of Information Management, Shih Chien University Kaohsiung Campus, Kaohsiung City, Taiwan
| | - Shin-Li Lu
- Department of Industrial Management and Enterprise Information, Aletheia University, New Taipei City, Taiwan
| | - Chien-Tzu Liao
- Department of Air Transporation Industry, Aletheia University, New Taipei City, Taiwan
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Economic-Statistical Performance of Auxiliary Information-Based Maximum EWMA Charts for Monitoring Manufacturing Processes. MATHEMATICS 2022. [DOI: 10.3390/math10132320] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
An auxiliary information-based maximum exponentially weighted moving average chart, namely, the AIB-MaxEWMA chart, is superior to the existing MaxEWMA chart in detecting small process mean and/or variability shifts. To date, AIB-MaxEWMA chart was designed based on the statistical perspective, which ignores the cost of process monitoring. The economic-statistical performance of the AIB-MaxEWMA chart for monitoring process shifts is investigated. The Monte Carlo simulation was conducted to determine the optimal decision variables, such as sample size, sampling interval, control limit constant, and smoothing constant, by minimizing the expected cost function under the statistical constraints. Numerical simulations indicate that when an auxiliary variable is highly related to the study variable, AIB-MaxEWMA charts not only have better statistical performance, but also have lower expected costs than MaxEWMA charts. Sensitivity analyses also show that a larger expected time to sample an auxiliary variable results in larger optimal expected costs and lower optimal sample size and sampling interval. The relationship between optimal decision variables and minimal costs is valuable for reference by researchers or process engineers.
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Alevizakos V, Chatterjee K, Koukouvinos C, Lappa A. A double generally weighted moving average control chart for monitoring the process variability. J Appl Stat 2022; 50:2079-2107. [PMID: 37434629 PMCID: PMC10332243 DOI: 10.1080/02664763.2022.2064977] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 04/03/2022] [Indexed: 10/18/2022]
Abstract
In the present article, a double generally weighted moving average (DGWMA) control chart based on a three-parameter logarithmic transformation is proposed for monitoring the process variability, namely the S 2 -DGWMA chart. Monte-Carlo simulations are utilized in order to evaluate the run-length performance of the S 2 -DGWMA chart. In addition, a detailed comparative study is conducted to compare the performance of the S 2 -DGWMA chart with several well-known memory-type control charts in the literature. The comparisons indicate that the proposed one is more efficient in detecting small shifts, while it is more sensitive in identifying upward shifts in the process variability. A real data example is given to present the implementation of the new S 2 -DGWMA chart.
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Affiliation(s)
- Vasileios Alevizakos
- Department of Mathematics, National Technical University of Athens, Zografou, Greece
| | - Kashinath Chatterjee
- Department of Population Health Sciences, Division of Biostatistics and Data Science, Augusta University, Augusta, GA, USA
| | - Christos Koukouvinos
- Department of Mathematics, National Technical University of Athens, Zografou, Greece
| | - Angeliki Lappa
- Department of Mathematics, National Technical University of Athens, Zografou, Greece
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Affiliation(s)
| | | | - W. L. Teoh
- School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya, Malaysia
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Kumar N, Singh RK. A comparative study of ANI- and ARL-unbiased geometric and CCC G control charts. Seq Anal 2021. [DOI: 10.1080/07474946.2020.1823194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Nirpeksh Kumar
- Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India
| | - Ranjeet K. Singh
- Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India
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Abstract
Recently, a homogeneously weighted moving average (HWMA) chart has been suggested for the efficient detection of small shifts in the process mean. In this study, we have proposed a new one-sided HWMA chart to effectively detect small changes in the process dispersion. The run-length (RL) profiles like the average RL, the standard deviation RL, and the median RL are used as the performance measures. The RL profile comparisons indicate that the proposed chart has a better performance than its existing counterpart’s charts for detecting small shifts in the process dispersion. An application related to the Dhahran wind farm data is also part of this study.
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A New Sum of Squares Exponentially Weighted Moving Average Control Chart Using Auxiliary Information. Symmetry (Basel) 2020. [DOI: 10.3390/sym12111888] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The concept of control charts is based on mathematics and statistics to process forecast; which applications are widely used in industrial management. The sum of squares exponentially weighted moving average (SSEWMA) chart is a well-known tool for effectively monitoring both the increase and decrease in the process mean and/or variability. In this paper, we propose a novel SSEWMA chart using auxiliary information, called the AIB-SSEWMA chart, for jointly monitoring the process mean and/or variability. With our proposed chart, the attempt is to enhance the performance of the classical SSEWMA chart. Numerical simulation studies indicate that the AIB-SSEWMA chart has better detection ability than the existing SSEWMA and its competitive maximum EWMA based on auxiliary information (AIB-MaxEWMA) charts in view of average run lengths (ARLs). An illustrated example is used to demonstrate the efficiency of the proposed AIB-SSEWMA chart in detecting small process shifts.
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Process monitoring using inflated beta regression control chart. PLoS One 2020; 15:e0236756. [PMID: 32730316 PMCID: PMC7392223 DOI: 10.1371/journal.pone.0236756] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 07/11/2020] [Indexed: 11/23/2022] Open
Abstract
This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.
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Affiliation(s)
- Manuel Cabral Morais
- Department of Mathematics & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
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Affiliation(s)
- Waqas Munir
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Abdul Haq
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
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Affiliation(s)
- Yi-Hua Tina Wang
- Department of Statistics, Tamkang University, New Taipei City, Taiwan
| | - Hsiuying Wang
- Institute of Statistics, National Chiao Tung University, Hsinchu, Taiwan
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Zhang J, He C, Li Z, Wang Z. Likelihood ratio test-based chart for monitoring the process variability. COMMUN STAT-SIMUL C 2015. [DOI: 10.1080/03610918.2014.957845] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Jiujun Zhang
- Department of Mathematics, Liaoning University, Shenyang, P.R. China
| | - Chuan He
- Department of Mathematics, Northeastern University, Shenyang, P.R. China
| | - Zhonghua Li
- Institute of Statistics and LPMC, Nankai University, Tianjin, P.R. China
| | - Zhaojun Wang
- Institute of Statistics and LPMC, Nankai University, Tianjin, P.R. China
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Zafar RF, Abbas N, Riaz M, Hussain Z. Progressive Variance Control Charts for Monitoring Process Dispersion. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2012.717668] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Shamsuzzaman M, Wu Z. Design of EWMA control chart for minimizing the proportion of defective units. INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2012. [DOI: 10.1108/02656711211270379] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Graham M, Mukherjee A, Chakraborti S. Distribution-free exponentially weighted moving average control charts for monitoring unknown location. Comput Stat Data Anal 2012. [DOI: 10.1016/j.csda.2012.02.010] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Graham M, Chakraborti S, Human S. A nonparametric exponentially weighted moving average signed-rank chart for monitoring location. Comput Stat Data Anal 2011. [DOI: 10.1016/j.csda.2011.02.013] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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