UNION INTERSECTION TEST IN INTERPRETING SIGNAL FROM MULTIVARIATE CONTROL CHART

Statistical Process Control (SPC) has been a very important discipline in quality control study since pioneered by Walter A. Shewhart in 1920s. Control charting is one of the important tools in SPC and has received wide attention from researchers as well as practitioners. The complexity and the impracticality in monitoring several univariate control charts for a multivariate process has made many practitioners use a multivariate control chart instead. Its usage gives a better control of the overall Type I error and the interdependency among variables is retained. Unfortunately, a multivariate control chart is not able to pinpoint the responsible variable(s) once an out-of-control (OOC) signal is triggered. Many diagnostic methods have been proposed to overcome this problem but all of them have their own limitations and drawbacks. The applicability of a diagnostic method for a limited number of variables, lack of physical interpretation, the complexity of the computation procedure and lack of location invariance are among the factors that have inhibited the implementation of multivariate charts. Lack of comparative studies for various diagnostic methods also makes it difficult for practitioners to choose an appropriate diagnostic method. This study highlights some problems that might arise in a comparison of diagnostic methods and makes suggestions to overcome them, hence, making the results of a comparative study more relevant and reliable. The effects of several factors such as the size of the deviation in a mean vector, the combination of various sizes of shifts in a mean vector and the inter-correlation among the variables on the performance of diagnostic methods are studied and a summary of the suitability of certain diagnostic methods for certain situations is given. This study presents a new comparison involving two diagnostic methods adapted from the methods proposed by Doganaksoy, Faltin and Tucker (1991) and Maravelakis et al. (2000). A problem related to the usage of eigenvectors with similar eigenvalues is revealed in this study and suggestions from previous studies regarding this matter are presented. Due to lack of multivariate approaches in dealing with the interpretation of a multivariate control chart signal, this study proposes a new method which embraces the principles of Union Intersection Test (UIT) in diagnosing an OOC signal. A thorough discussion of the UIT principle, the hypotheses, the test statistic and the application of the union intersection technique in the diagnosis problem is presented. An extension of the first comparison study is which includes the proposed method is carried out. The performance of the new diagnostic method is studied and its strengths and weaknesses are discussed. A simplified version for the new method, involving application of spectral decomposition, is also proposed. By using this simplified approach, the common practice of considering multiple types of covariance matrices in a comparison study of diagnostic methods can be avoided to some extent. This study is concluded with a few suggestions of potential further work

Numerical solution of SOR iterative method for fuzzy Fredholm integral equations of second kind

In this paper, we deal with the application of Successive Over-Relaxation (SOR) iterative method for solving fuzzy Fredholm integral equations of the second kind (FFIE-2). In addition to that, we apply the trapezoidal rule to derive the approximate solution of FFIE-2 which consists of a system of integral equations. Next, the approximate equation is used to develop a system of linear equations. Then, we consider SOR iterative method to solve the generated system of linear equations. Next, SOR iterative method is implemented on some numerical examples. Finally, the numerical results is discussed in details by comparing the number of iterations, the computational time, and the Hausdorff distance to analyze the performance of proposed method. Based on the numerical results obtained from all the numerical examples by using Gauss-Seidel (GS) and SOR methods, it can be pointed out that SOR method is more efficient than the GS method

An Application of Univariate and Multivariate Control Charts in Monitoring Water Quality

Control chart is a tool for detecting an out-of-control signal in statistical process control (SPC). It is widely used in process monitoring in order to detect changes in process mean or process dispersion. This study aims to illustrate the application of multivariate control charts in monitoring water quality at one of the water treatments plants in Kota Kinabalu, Sabah. The tested water quality variables in this study are turbidity, pH value, dissolved oxygen (DO) and concentration of ferum. Two multivariate control charts, Hotelling’sT2 and MCUSUM control charts are constructed under the violation of the multivariate normality assumption. The purpose is to study the effect of non-normal data upon the monitoring process using the selected multivariate control charts. By comparing the monitoring process between the two types of control charts, the consistency of the results is studied. All the univariate and multivariate control charts produced out-of-control signals from different points, hence inconclusive results obtaine

SOR Iterative Method with Simpson’s 1/3 Rule for the Numerical Solution of Fuzzy Second Kind Fredholm Integral Equations

In this study, we present the application of Successive Over-Relaxation (SOR) iterative method to solve fuzzy Fredholm integral equations of the second kind (FFIE-2). In addition to that, the Simpson’s 1/3 quadrature rule is applied to derive the approximate solution of FFIE-2. Then, we use the approximate equation to generate a system of linear equations. Next, SOR iterative method is introduced to solve the generated system of linear equations. Moreover, we conduct some numerical examples to illustrate the applicability of the SOR iterative method. Finally, we discuss the efficiency of the proposed method by comparing the number of iterations, computational time and Hausdorff distance. Based on the numerical results, we conclude that SOR method is better than Jacobi and Gauss-Seidel iterative methods

Predicting academic performance of undergraduate students through collective self-esteem and group trust

This study was motivated by the concern that how group positiveness could potentially give an impact upon academic achievement of students. In specific, this study attempted to investigate effects of collective self-esteem (CSE), group trust (GT), and each domain of CSE and GT upon academic achievement. This study also aims to compare the effects of CSE, GT and each of their domains between male and female students. Eight hundred and sixty nine students from various faculties in Universiti Malaysia Sabah voluntarily participated in the study. CSE was measured through the Collective Self-Esteem Scale by Luhtanen and Crocker (1992) and GT was measured through Trust in Team Scale by Adams, Waldher and Sartori (2008). Both of the scales contain 4 domains. Membership SelfEsteem, Private Self-Esteem, Public SelfEsteem, and Importance to Identity are the domains for CSE. Whilst, GT are comprised of Competence, Integrity, Benevolence, and Predictability. Academic performance was measured by the students’ Cumulative Grade Point Average (CGPA) in Semester I, 2019. Descriptive data analysis, correlation analysis and multiple regression analysis have been conducted and the results showed that overall scores of CSE and GT had no effects on the CGPA. However, in the second attempt, 2 of the CSE domains, i.e. Membership and Importance to identity contributed significantly towards CGPA. Interestingly, further results revealed that low score of Competence turned out to be the most significant GT predictor towards CGPA in both males and female students. These findings suggest that positive feelings derived from group belongingness and trust given to group members could boost the academic success of students

A new distance measure and corresponding TOPSIS method for interval-valued intuitionistic fuzzy sets in multi-attribute decision-making

Strengthening the evaluation of teaching satisfaction plays a crucial role in guiding teachers to improve their teaching quality and competence, as well as in aiding educational institutions in the formulation of effective teaching reforms and plans. The evaluation process for teaching satisfaction is usually regarded as a typical multi-attribute decision-making (MADM) process, which inherently possesses uncertainty and fuzziness due to the subjective nature of human cognition. In order to improve the subtle discrimination of evaluation information data and enhance the accuracy of the evaluation results, we have developed an integrated MADM method by combining a new distance measure and an improved TOPSIS method for interval-valued intuitionistic fuzzy sets (IvIFSs). First, a novel distance measure for IvIFSs based on triangular divergence is proposed to capture the differences between two IvIFSs, and some properties of this distance measure are investigated. Then, the superiority of this new distance measure is compared with some existing distance measures. Afterward, an improved TOPSIS method is also established based on the proposed triangular distance under the interval-valued intuitionistic fuzzy setting. Besides, to illustrate the practicality of the new method, a numerical example is presentedto evaluate mathematics teaching satisfaction. Moreover, a comparative analysis that includes existing TOPSIS methods, is presented to demonstrate the superiority of the given method. The comparison outcomes show that the proposed technique can effectively discern uncertainties or subtle differences in IvIFSs, resulting in more accurate and comprehensive evaluation results for teaching satisfaction. Overall, the findings of this study emphasize the importance of incorporating the new distance measure in MADM. The proposed approach serves as a valuable tool for decision-makers to compare and evaluate alternatives effectively

Structural equation modelling in investigating the role of academic motivation upon academic achievement

Academic achievement is the degree to which students, educators, or organizations have attained their desired learning goals, whether short-term or long-term. It provides evidence of institutional efficiency in producing knowledgeable, proficient, and marketable graduates. Understanding the factors contributing to students' success is an important task not only for the students or lecturers but also for higher learning institutions. This understanding serves as valuable input for designing effective teaching, learning, and student activities to improve academic performance and reduce academic failure. Thus, the current study sought to determine the direct and indirect effects of self-esteem, personality traits, and emotional intelligence, as well as examine the role of academic motivation on students' learning outcomes as a mediator. A stratified random sampling method was employed, and 533 undergraduate students participated in this study. Four standard instruments have been adopted for data collection, which are Rosenberg Self-Esteem Scale (RSES), Schutte SelfReport Emotional Intelligence Test (SSEIT), Big Five Inventory (BFI), and Academic Motivation Scale. Structural equation modelling (SEM) was used to identify the relationship between selfesteem, personality traits, and emotional intelligence on academic achievement and examine academic motivation as a potential mediator for academic achievement. The findings of this study revealed that academic motivation, emotional expression, and conscientiousness were significant factors. Moreover, negative self-esteem, conscientiousness, openness, and selfemotional regulation exhibited significant indirect effects on academic achievement, and academic motivation has been proven to serve as a significant mediator. These results revealed essential inputs and provided a greater understanding of the higher learning institutions in structuring and planning their students' support systems and activities. Given the significant role of academic motivation as a mediator, it will be interesting to discover its significant contributors. Further studies can be conducted to determine the differences in academic motivation contributing factors with regard to gender, discipline, and socioeconomic backgrounds

Probabilistic linguistic multi-attribute decision making approach based upon novel GMSM operators

Probabilistic linguistic terms set (PLTS), a new tool for expressing uncertain decision information, is composed of all possible linguistic terms (LTs) and their related probabilities. It also increases the corresponding probability of LTs in hesitant fuzzy linguistic term set (HFLTS). On the other hand, aggregation operator is an important information fusion tool, the Maclaurin symmetric mean (MSM) operator can provide more flexibility and robustness in information fusion and make it more suitable for solving MADM problems with independent attributes. This current study adopts the merits of PLTS and MSM operator, and then a novel probabilistic linguistic decision-making approach are targeted. Firstly, the operations of two PLTSs are redefined based upon Archimedean t-norm (ATN) and Archimedean t-conorm (ATC); Secondly, the probabilistic linguistic generalized MSM operator (PLGMSM) is proposed based on ATN and ATC, some properties of PLGMSM are investigated, then some special PLGMSM operators have been studied in detail when the parameters take different values and the generator of ATN takes different functions. Thirdly, the weighted probabilistic linguistic generalized MSM operator (WPLGMSM) is studied along with some properties of PLGMSM, some special WPLGMSM operators have been also investigated in detail when the parameters take different values and the generator of ATN takes different functions. Finally, on the basis of our proposed aggregation operators, the aggregated-based decision-making approach is designed and an example is supplied to manifest the effectiveness of the proposed approach. Furthermore, some comparison analyses with extant decision approaches are carried out to illustrate the validity and feasibility of the proposed approach