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Adaptive CUSUM Location Control Charts Based on score functions: An Application in Semiconductor Wafer Field

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022年第3期47卷 3725-3749页

作者： Zaman, Babar Riaz, Muhammad Abujiya, Mu'azu Ramat Lee, Muhammad Hisyam Univ Teknol Malaysia Dept Math Sci Skudai Malaysia Univ Hafir Al Batin Coll Sci Dept Math Hafir Al Batin Saudi Arabia King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran Saudi Arabia King Fahd Univ Petr & Minerals Preparatory Year Math Program Dhahran Saudi Arabia

An adaptive CUSUM (ACUSUM) control chart got special attention against classical CUSUM control chart to detect a shift of different sizes in the process location. Similarly, an ACUSUM based on classical EWMA statistic and score function, denoted as a ACUSUM E control chart, is improved form of classical CUSUM control chart and can identify different sizes of shift. Classical EWMA statistic in ACUSUM(E) control chart fails to offer clear instruction for parameter values to identify a precise shift as the classical CUSUM statistic does. To address this issue, this study proposed two ACUSUM control charts, symbolized as ACUSUM(C)((1)) and ACUSUM(C)((2)) to further improve detection ability of shift in the process location. Novelty of the proposed control charts is to initially adaptively renew reference parameters values based on classical CUSUM statistic and then to assign a weight on it using score functions. An algorithm is developed in MATLAB using Monte Carlo simulation method to obtain numerical results. Based on numerical results, performance measures such as average run length for a specific shift, extra quadratic loss, relative average run length, and performance comparison index for overall performance are calculated for comparison purpose. Comparison based on visual presentation and numerical results reveals the proposed control charts performed quite effective against some existing control charts. It is worthy to mention, classical CUSUM control chart is special cases of proposed ACUSUM(C)((1)) control charts at specific values of parameter. Finally, proposed control charts are also implemented on real-life data to show practical significance to users and practitioners.

关键词： Adaptive CUSUM Performance measures Monte Carlo simulation score functions

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Optimizing process monitoring: Adaptive CUSUM control chart with hybrid score functions

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Measurement 2025年 254卷

作者： Babar Zaman Syed Zeeshan Mahfooz Naveed Khan Saddam Akber Abbasi Faculty of Engineering Sciences Ghulam Ishaq Khan Institute of Engineering Sciences and Technology Khyber Pakhtunkhwa Pakistan Dept. of Computer Sc. and Engr. University of Hafar Al-Batin Saudi Arabia Department of Mechanical Engineering University of Hafr Al Batin Hafr Al Batin Saudi Arabia Department of Mathematics and Statistics College of Arts and Sciences Qatar University Qatar

The Cumulative Sum (CUSUM) Control Chart (CC) is a powerful tool for detecting small to moderate shifts in process parameters. While the traditional CUSUM CC determines the shift magnitude, it may not effectively handle a wide range of shifts encountered in real-world applications. To address this, an adaptive CUSUM (ACUSUM) CC has been developed. This study introduces a novel ACUSUM CC by integrating Huber and Bi-square score functions, which possess unique attributes such as monotonicity and redescending properties. Despite their individual advantages, limited research has explored their combined use in ACUSUM CC design. By amalgamating these functions into a unified formulation, we propose an innovative ACUSUM CC capable of effectively monitoring shifts of varying magnitudes in the process location parameter. The proposed CC is assessed through Monte Carlo simulations under both zero-state and steady-state conditions. Key performance metrics, including Average Run Length (ARL), median run length (MDRL), and Standard Deviation of Run Length (SDRL), are used to evaluate the ability of the proposed CC to detect individual shifts. Additionally, relative ARL, extra quadratic loss, and the process capability index are utilized to measure efficiency across a range of shifts, ensuring a comprehensive performance evaluation. A comparative analysis based on performance metrics and visual representations highlights the superior performance of the proposed CC over conventional methods. Furthermore, its application in energy usage analysis demonstrates its effectiveness in detecting anomalies, supporting proactive decision-making for optimizing energy consumption and resource allocation. These findings confirm the practicality, reliability, and enhanced monitoring capabilities of the proposed ACUSUM CC in real-world industrial and environmental scenarios.

关键词： Adaptive Monitoring Anomaly Detection CUSUM Control Chart Hybrid score Function Process Mean Shift Quality Control score functions

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Enhanced MCDM Based on the TOPSIS Technique and Aggregation Operators Under the Bipolar pqr-Spherical Fuzzy Environment: An Application in Firm Supplier Selection

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APPLIED SCIENCES-BASEL 2025年第7期15卷 3597-3597页

作者： Ameen, Zanyar A. Salih, Hariwan Fadhil M. Alajlan, Amlak I. Mohammed, Ramadhan A. Asaad, Baravan A. Univ Duhok Coll Sci Dept Math Duhok 42001 Iraq Qassim Univ Coll Sci Dept Math Buraydah 51452 Saudi Arabia Univ Duhok Coll Basic Educ Dept Math Duhok 42001 Iraq Univ Zakho Coll Sci Dept Math Zakho 42002 Iraq Cihan Univ Duhok Coll Sci Dept Comp Sci Duhok 42001 Iraq

Multiple criteria decision-making (MCDM) is a significant area of decision-making theory that certainly warrants attention. It might be difficult to accurately convey the necessary decision facts when navigating decision-making problems since we frequently run into complicated issues and unpredictable situations. To address this, introducing the novel idea of the bipolar pqr-spherical fuzzy set (BpqrSFS), a hybrid structure of the bipolar fuzzy set (BFS) and the pqr-spherical fuzzy set (pqr-SFS), is the main goal of this work. The fundamental (set-theoretic and algebraic) operations on BpqrSFSs are explained as well as their relations to several known models. A distance measure, such as Euclidean distance, among BpqrSFNs, is provided. Afterward, we expand the fundamental aggregation operators to the pqr-spherical fuzzy (BpqrSF) environment by developing bipolar pqr-spherical fuzzy-weighted averaging and bipolar pqr-spherical fuzzy-weighted geometric operators for aggregating BpqrSFNs. According to the aforementioned distance measure and operators, an MCDM approach is established consisting of two algorithms, namely, the TOPSIS method and the method using the proposed operators in the BpqrSF context. Moreover, a numerical example is provided in order to ensure that the presented model is applicable. By using the two algorithms, a comparative analysis of the proposed method with other existing ones is given in order to verify the feasibility of the suggested decision-making procedure.

关键词： bipolar fuzzy set r,s,t-spherical fuzzy sets bipolar pqr-spherical fuzzy sets score functions aggregation operators TOPSIS decision making

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NA Operator-Based Interval-Valued q-Rung Orthopair Fuzzy PSI-COPRAS Group Decision-Making Method

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2023年第1期25卷 198-221页

作者： Zhang, Xiaolu Dai, Li Wan, Benting Jiangxi Univ Finance & Econ Sch Stat Nanchang 330013 Jiangxi Peoples R China Jiangxi Univ Finance & Econ Sch Software & Internet Things Engn Nanchang 330013 Jiangxi Peoples R China

Interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs) have been widely used to address uncertain or imprecision data in practical decision-making. One contribution of this study is to develop a new score function for comparing the magnitude of IVq-ROFNs. We construct the variance value-based index for analyzing different score functions and the results show that the developed score function well improves the fluctuation of IVq-ROFNs and has much stronger ability to distinguish IVq-ROFNs. The second contribution is that interval-valued q-rung orthopair fuzzy neutral operational law is investigated and a new interval-valued q-rung orthopair fuzzy weighted average neutral aggregating (IVq-ROFWANA) operator is proposed. We conduct a detail comparison analysis with the existing operators and show that the calculated results obtained by them are consistent. The third contribution is that a new interval-valued q-rung orthopair fuzzy preference selection index and complex proportional assessment (PSI-COPRAS) method is developed. On the one hand, we propose the similarity-proximity degree based-weight determination method for identifying the experts' weights and modify the classical PSI method to identify weights of attributes under IVq-ROFNs environments. On the other hand, we introduce interval-valued q-rung orthopair fuzzy COPRAS to rank alternatives. Finally, the proposed method is implemented in warning risk evaluation of hypertension in residents to demonstrate its applicability. Comparing with the classical TOPSIS, MOORA and MABAC, the biggest advantage of the developed method is that that it can not only fully consider the influences of the maximum and minimum attribute indices but also allow both the weights of attributes and experts to be completely unknown in advance.

关键词： Interval-valued q-rung orthopair fuzzy set COPRAS NA operator score functions

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A complete ranking of trapezoidal-valued intuitionistic fuzzy number: an application in evaluating social sustainability

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NEURAL COMPUTING & APPLICATIONS 2023年第8期35卷 5939-5962页

作者： Jeevaraj, S. Rajesh, R. Nayagam, V. Lakshmana Gomathi Atal Bihari Vajpayee Indian Inst Informat Technol Dept Appl Sci Math Gwalior 474015 Madhya Pradesh India Atal Bihari Vajpayee Indian Inst Informat Technol Dept Management Studies DoMS Gwalior 474015 Madhya Pradesh India Natl Inst Technol Tiruchirappalli Dept Math Tiruchirappalli 620015 Tamil Nadu India

Conventional trapezoidal intuitionistic fuzzy numbers (CTrIFNs) are used in the literature to handle many real-life problems with imprecise information. However, the CTrIFNs are not the real generalization of interval-valued intuitionistic fuzzy numbers (IVIFNs) and triangular intuitionistic fuzzy numbers (TIFNs). This study discusses the non-conventional trapezoidal intuitionistic fuzzy numbers called trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) that generalize (contain) all real-valued intuitionistic fuzzy numbers, IVIFNs and TIFNs. Various researchers worldwide are looking for a complete ranking principle on the set of TrVIFNs. However, none of them yields a complete ranking. The paper's main aim is to propose a new complete ranking principle on the class of TrVIFNs. The complete ranking principle on the set of TrVIFNs makes the decision-making algorithm more robust. To achieve the main aim, firstly, we introduce eight different score functions on the set of TrVIFNs and study their mathematical properties. Secondly, we present a new ranking principle by considering all eight score functions in a linear order. Further, we prove (mathematically) that the introduced ranking principle defines complete ranking on the set of TrVIFNs. Thirdly, we show the significance of the proposed method compared with the existing methods on various classes of fuzzy and intuitionistic fuzzy numbers. Finally, we implement a case application of the proposed complete ranking principle for evaluating the social sustainability performance of Indian firms.

关键词： Trapezoidal-valued intuitionistic fuzzy number Social sustainability score functions Complete ranking principle

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Adaptive CUSUM control charts for efficient monitoring of process dispersion

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2022年第5期38卷 2273-2302页

作者： Zaman, Babar Univ Hafr Al Batin Coll Sci Dept Math Hafar al Batin Saudi Arabia

An adaptive cumulative sum (ACUSUM) control chart is an advance form of the classical CUSUM control chart to identify different sizes of shift in the process parameters (location and/or dispersion). In the continuation of the ACUSUM control chart, this study also proposed ACUSUM control charts to enhance the performance of the process dispersion for a broad range of shift. The proposed ACUSUM control charts methodologies are based on the dispersion CUSUM statistic, score (Huber and Bi-square) functions, generalized likelihood ratio test, and nonlinear optimization technique. The use of dispersion CUSUM statistic helps to distinguish a specific shift as the classical CUSUM statistic does, the score functions, the nonlinear optimization technique and generalized likelihood ratio test enhance the ability of the proposed ACUSUM control charts to distinguish a shift of different size. For the assessment of control charts, run length (RL) measure is used, and it is generated by developing an algorithm in MATLAB through Monte Carlo simulation method. Further, average of RL is utilized to carry out comparative analysis of control charts for a single shift, while for a certain range of shift (comprehensive analysis), extra quadratic loss (EQL), relative average run length (ARL), and performance comparison index (PCI) measures are used. Findings based on numerical results and visual presentations reveal the superiority of the proposed control charts against some existing control charts. Moreover, for real-world point of assessment, the proposed control chart is implemented with numerical data to show the worth over other control charts.

关键词： adaptive control charts generalized likelihood ratio test monte carlo simulation nonlinear optimization technique performance evaluation measures score functions

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Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2022年第6期24卷 2889-2904页

作者： Reig-Mullor, Javier Salas-Molina, Francisco Univ Miguel Hernandez Elche Av Univ S-N Elche 03202 Spain Univ Politecn Valencia Alcoy 03801 Spain

The concept of fuzzy set has been extended by neutrosophic fuzzy sets to represent sets whose elements have different degrees of membership characterized by a truth-membership function, an indeterminacy-membership function and a falsity-membership function. It is usually assumed that these functions are linear, hence excluding the possibility of non-linearity in many decision-making situations. From an alternative definition of non-linear neutrosophic numbers, we develop the concepts of (alpha, beta, gamma)-cuts, possibility mean, variance, skewness and a new possibility score function. These concepts are useful to deal with multiple criteria decision making problems. We illustrate the practical use of these concepts by means of a real case study in supply chain risk management in the motor industry. Due to the fact that neutrosophic sets have been used in several areas of decision-making, finance and economics, we argue that our proposal contributes to enhance the application of neutrosophic numbers.

关键词： Neutrosophic numbers Non-linearity Multiple criteria decision making score functions

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Aggregation of Individual Rankings Through Fusion functions: Criticism and Optimality Analysis

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2022年第3期30卷 638-648页

作者： Bustince, Humberto Bedregal, Benjamin Jesus Campion, Maria da Silva, Ivanosca Fernandez, Javier Indurain, Esteban Raventos-Pujol, Armajac Santiago, Regivan H. N. Univ Publ Navarra Dept Estad Informat & Matemat Pamplona 31006 Spain Univ Publ Navarra Inst Smart Cities Pamplona 31006 Spain Univ Fed Rio Grande Norte UFRN Dept Informat & Matemat Aplicada DIMAp BR-59078970 Natal RN Brazil Univ Publ Navarra Inst Adv Res Business & Econ Pamplona 31006 Spain Univ Fed Rio Grande Norte UFRN Diretoria Mat & Patrimonio DMP BR-59078970 Natal RN Brazil Univ Publ Navarra InaMat2 Inst Adv Mat & Math Pamplona 31006 Spain Univ Publ Navarra Inst Adv Res Business & Econ Pamplona 59078970 Spain

Throughout this article, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first, we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice-where well-known impossibility results as the Arrovian ones are encountered-and the decision-making approaches-where the necessity of fusing rankings is unavoidable. Moreover, it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then, we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice, one should look for the maximal elements with respect to such orders defined on rankings.

关键词： Decision making Proposals Mathematics Aggregates Smart cities Organizations Indexes Aggregation decision-making general means ranking ranking optimality score functions social choice

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Adaptive Memory Control Charts Constructed on Generalized Likelihood Ratio Test to Monitor Process Location

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022年第11期47卷 15049-15081页

作者： Zaman, Babar Lee, Muhammad Hisyam Riaz, Muhammad Abujiya, Mu'azu Ramat Mehmood, Rashid Abbas, Nasir Univ Hafr Al Batin Coll Sci Dept Math Hafar al Batin Saudi Arabia Univ Teknol Malaysia Dept Math Sci Skudai Malaysia King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran Saudi Arabia King Fahd Univ Petr & Minerals Preparatory Year Math Program Dhahran Saudi Arabia

An adaptive cumulative sum (CUSUM) control chart based on the classical exponential weighted moving average (EWMA) statistic and Huber's function, symbolized as an ACUSUME control chart, is an enhanced form of the classical CUSUM control chart that can identify different sizes of shift. However, the classical EWMA statistic for the ACUSUME control chart does not provide explicit rule for parameter choices to diagnose a specific shift. To overcome this issue, this study has proposed two ACUSUM control charts, symbolized as ACUSUM(c) control charts to monitor a specific and a certain range of shift. The novelty behind the proposed ACUSUM(c) (ACUSUM(c)((1)) and ACUSUM(c)((2))) control charts is initially adaptively updating the reference parameter using the classical CUSUM statistic, generalized likelihood ratio test, and score functions to achieve superior performance. An algorithm in MATLAB using the Monte Carlo simulation technique is designed to obtain numerical results. Furthermore, based on numerical results, performance evaluation measures such as average run length, extra quadratic loss, relative average run length, and comparison index are calculated. The proposed ACUSUM(C) control charts based on performance evaluation measures and visual presentation are compared against other control charts. Findings reveal the superiority of the proposed ACUSUM(C) control charts. Besides, for practical point of view, the proposed ACUSUM(C)((1)) control chart is implemented with numerical data to show the significance over other control charts.

关键词： Adaptive Generalized likelihood ratio test Monte Carlo simulation Performance evaluation measures score functions

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Robust design optimization under dependent random variables by a generalized polynomial chaos expansion

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2021年第5期63卷 2425-2457页

作者： Lee, Dongjin Rahman, Sharif Univ Iowa Dept Mech Engn Iowa City IA 52242 USA

New computational methods are proposed for robust design optimization (RDO) of complex engineering systems subject to input random variables with arbitrary, dependent probability distributions. The methods are built on a generalized polynomial chaos expansion (GPCE) for determining the second-moment statistics of a general output function of dependent input random variables, an innovative coupling between GPCE and score functions for calculating the second-moment sensitivities with respect to the design variables, and a standard gradient-based optimization algorithm, establishing direct GPCE, single-step GPCE, and multi-point single-step GPCE design processes. New analytical formulae are unveiled for design sensitivity analysis that is synchronously performed with statistical moment analysis. Numerical results confirm that the proposed methods yield not only accurate but also computationally efficient optimal solutions of several mathematical and simple RDO problems. Finally, the success of conducting stochastic shape optimization of a steering knuckle demonstrates the power of the multi-point single-step GPCE method in solving industrial-scale engineering problems.

关键词： RDO Second-moment analysis GPCE Design sensitivity analysis score functions Stochastic optimization

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