Theses & Dissertations
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PublicationShooting-euler method for two-point fuzzy boundry value problems(Universiti Malaysia Perlis (UniMAP), 2016)Differential equation plays an important role in modeling of real world problems. However, many real world problems involved are very difficult to obtain clear and exact model. Therefore, differential equation with fuzzy set is essential to provide better understanding. In this study, a two-point fuzzy boundary value problem (FBVP) is considered and solved numerically by using the shooting method. First, the FBVP is interpreted under the concept of generalized differentiability and then followed by reducing it into parametric forms, which fmally obtained four different cases. For each case, the shooting method is used to construct the general procedure of obtaining solutions. Then, Euler method is used to approximate the fmal solutions. A numerical example is provided in order to show the application of the proposed procedures. All numerical simulations are executed by using MA TLAB. From numerical results, it is clear that the approximate solutions obtained by using the proposed procedures are slightly different compared to analytical solutions obtained by using Adomian decomposition method (ADM). Since the values close to each other, thus it can be concluded that the proposed procedure is applicable to solve any two-point FBVP under the concept of generalized differentiability.
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PublicationReliability simulation of scheduled preventive maintenance for surface-mount technology machine(Universiti Malaysia Perlis (UniMAP), 2016)This thesis presents an improved maintenance approach for the surface-mount technology; particularly the AX-50 I machine's scheduled of preventive maintenance by using reliability simulation. This is to predict the failure of the machine and estimate the probability that the machine will not fail over some operational time in order to maintain its functional from sudden breakdown, especially during critical time. The main aim of this study is to propose a better schedule of preventive maintenance than current schedule which is once a month based on the machine's reliability. Data source is collected from July 2014 until June 2015 for 24 hours (2 shifts) of working day from Monday to Sunday. The mathematical model used in this study is based on reliability and model simulation was developed by using Arena software. In conclusion, the best scheduled preventive maintenance for this machine is once for every two weeks. This frequency of scheduled preventive maintenance totally reduces the machine's breakdown as it will extend machine's re1iability and its lifespan thus prolong machine's time to fail.
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PublicationDifferential transformation method (DTM) for solving SIS and SI epidemic models(Universiti Malaysia Perlis (UniMAP), 2015)Differential equations play an important role in modeling real world problem. One of the importance of differential equations is seen in the SIS and SIR epidemic models. Many researches have been proposed to solve SIS and SIR models numerically. However, there is no study about the application of Differential Transformation Method (DTM) for solving SIS and SI epidemic models. In this study, DTM is proposed to solve the SIS and SI epidemic models for constant population. Firstly, the theoretical background of DTM is studied and followed by constructing the solutions of SIS and SI epidemic models. Furthermore, the convergence analysis of DTM is proven by proposing two theorems. Finally, numerical computations are made and compare with the exact solution. From the numerical result, the solution produced by DTM approaches the exact solution which agreed with the proposed theorems. In summary, DTM is an alternative technique to be considered in solving many practical problems involving differential equations.
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PublicationOne dimensional heat transfer through rectangular fin using finite element method (FEM)(Universiti Malaysia Perlis (UniMAP), 2016)This dissertation present a study of heat transfer through rectangular fin by using finite element method. In solving heat related problem, there are many methods that can be used. This study will be focused on this area with the objectives to develop FEM algorithm using MATLAB for 1-D heat transfer problem. By applying this algorithm to solve 1-D heat transfer problem, we will compare both numerical and exact solution result. From here, the variables of different number of nodes, length and conductivity properties were tested to investigate the effect. By focusing on 1-Dimenesional heat equation, the Galerkin method is used. This study will apply numerical solution technique using FEM to solve !-dimensional heat transfer through rectangular fins and developed a suitable algorithm for computational purpose. As expected, the results obtain are coherent with the theory with a negligible difference. Overall, this research shows that the number of nodes can affect the accuracy of result however the difference is so small that it does not have much effect. Meanwhile, the length does not relate or affect the number of nodes and are independent variable. Lastly, the material properties are the only variable that can affect both number of nodes and length.
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PublicationThe modelling and simulation on burger production process: a case study in small and medium industry(Universiti Malaysia Perlis (UniMAP), 2015)This simulation study focuses on burger production process runs by a SMI (small and medium industry) located in Kedah. The aim of this study is to develop the current production line of the company in order to observe the performance of the system and then suggest the methods for improvement. The efficiency of the current system including the utilization of workstations and workers are estimated from the simulation result. The outputs of simulation are compared with the actual data for validity of the simulation model. This study enables the observation of Queuing Theory application in discrete-event simulation. Queuing Theory is used to develop the mathematical model of the production line. Based on the results from current simulation model, bottleneck of the system is identified. As the company plans to increase the production, therefore an improvement model is built to forecast the possible outcome of the increasing production capacity. The proposed actions are adding another machine at bottleneck point and adding more workers for speeding up the manual tasks. By adding the machine, the structure of multiple server queuing model is observed. The results from the improvement model shows 92%achievement from the targeted output whenever the machine is added. By increasing the number of workers, the total of finish product also increases with 98% from the target. Therefore, it can be concluded that the company is able to increase the production capacity by doing few adjustment on the current burger production system. From the study, methods to improve the production line and increase the production rate are identified where they need to add another forming machine and more workers to speed up the tasks.
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