Pusat Pengajian Sains Matematik - Tesis

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    MSG453 - Queuing System and Simulation February 2021
    (2021-02)
    PPSM, Pusat Pengajian Sains Matematik
    Please check that this examination paper consists of TEN (10) pages of printed material before you begin the examination. Instructions : Answer all FOUR (4) questions.
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    Development Of Robust Memory-Type Charts Under Repetitive Sampling And Triple Sampling Charts For The Gamma Process
    (2024-04)
    Mahmood, Yasar
    Production processes in modern industries usually produce products with small variations due to technological advancement. The Shewhart-type charts are insensitive in detecting small process shifts. By developing memory-type and adaptive-type charts, researchers have solved the shortcomings of the Shewhart-type charts in detecting small shifts. Also, due to high sampling costs and destructive testing, quality engineers use individual control charts to monitor the process mean. There are three objectives in this thesis. Firstly, the triple exponentially weighted moving average (TEWMA) scheme and Tukey control chart (TCC) are combined to develop the TEWMA-TCC and repetitive sampling (RS) based RS-TEWMA-TCC, to monitor the mean of normal and non-normal distributed processes. The TEWMA-TCC, RS-TEWMA-TCC and competing charts are compared based on average run length (ARL), standard deviation of the run length (SDRL) and median run length (MRL) metrics under both zero-state (ZS) and steady-state (SS) conditions. The TEWMA-TCC and RS-TEWMA-TCC display dominance in detecting mean shifts in both directions. They are also robust to skewed distributions in that they are devoid of the ARL-biased problem. Secondly, the RS for cumulative sum (CUSUM)-type statistics discussed by Riaz et al. (2017) is coupled with the Shewhart chart to propose the RS Shewhart exponentially weighted moving average CUSUM TCC (RS-SEC-TCC).
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    Modeling Of Curves And Surfaces Using Ght-Bernstein Basis Functions And Using Optimization Methods To Construct Developable Surfaces
    (2024-03)
    Bibi, Samia
    A Bézier model with shape parameters is an influential research topic in geometric modeling and CAGD. This thesis describes the construction of generalized hybrid trigonometric Bézier (GHT-Bézier) curves using generalized hybrid trigonometric Bernstein (GHT-Bernstein) basis functions with three shape parameters and their applications in geometric modeling. The recursive formula in explicit expression is used to generalize the hybrid trigonometric Bernstein basis functions of degree 2, and the new generalized hybrid trigonometric Bernstein basis functions contain all the geometric properties of traditional Bernstein basis functions. A class of GHT-Bézier developable surfaces is constructed by using the principle of duality between the planes and points. To improve the efficiency of complex engineering products, a developable surface with higher developability degree is necessary to be obtained. The optimization techniques named as Particle Swarm Optimization (PSO) technique and Improved-Grey Wolf (IGWO) technique are used to find the optimal shape parameters for determining developability degree. The developability degree of the surface is the objective function in optimization techniques. The modeling examples demonstrate the effectiveness of the proposed method with fairness of the surfaces. The developability degree obtained by PSO and I-GWO algorithm is given.
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    Steady Heat Conduction Solution Using Trigonometric Bezier Finite Element Method
    (2024-08)
    Abidin, Mohamad Naufal Zainal
    The Finite Element Method (FEM) is a numerical technique used to solve several forms of partial differential equations, which are commonly utilized in engineering and mathematical modelling. Basic polygons such as triangles and quadrilaterals are used as element shapes in FEM. Due to the rigid sides of these basic shapes, they have resulted in sharp edges and are limited in handling irregular or curved geometries. To address this issue, mesh refinement is required to maintain the original geometry of the model, resulting in a larger number of elements and an increase in computational time. The spline functions are used as basis functions in isogeometric Finite Element Analysis(FEA). Isogeometric analysis (IGA) is a technique that recently developed in computational mechanics that offers the possibility of integrating the analysis and the design process into a single and unified process. This technique has the advantage of providing seamless integration of accurate geometry, thus bridging the gap between computer-aided geometric design and finite element analysis. Commonly, nonuniform rational B-splines (NURBS) and Bernstein-Bézier are used as basis functions in IGA. However, in this study, Trigonometric Bézier basis function will be used to solve the heat conduction problem in a two-dimensional curvilinear duct pipe. In summary, the findings indicate that the results obtained using the Trigonometric Bézier method are promising. The mean error recorded is minimal compared to the existing method, namely the Bernstein Bézier.
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    Penalized Quantile Regression Methods And Empirical Mode Decomposition For Improving The Accuracy Of The Model Selection
    (2024-07)
    In this study, in several scientific studies, the variables of interest are often represented by time series processes, and such time series data are frequently non-stationary and non-linear, resulting in low accuracy of the resulting regression models and less reliable conclusions. In addition, the ordinary least squares method is sensitive to outliers and heavy-tailed errors in data, and several predictors may suffer from multicollinearity problems. Moreover, selecting the relevant variables when fitting the regression model is critical. Therefore, three methods based on a combination of the empirical mode decomposition (EMD) algorithm and penalized quantile regression have been proposed in this study. The EMD algorithm decomposes the non-stationary and non-linear time series data into a finite collection of approximately orthogonal components called intrinsic mode functions and residual components. In several studies, these components have been employed as novel predictor variables to study the behaviour of the response variable. This study aims to apply the proposed EMD-QRR, EMD-QR, and EMD-QREnet methods to identify the influence of the decomposition components of the original predictor variables on the response variable to build a model that has the best fit and improve prediction accuracy. Furthermore, this study deals with the multicollinearity issue between the decomposition components. To verify the prediction performance of the proposed methods, the proposed methods are compared with three existing regression methods used in previous studies. Simulation studies and empirical analysis of the real data were carried out in this study.