A bi-objective dynamic model for multi-state weighted k-out-of-n system reliability
- Authors: Khorshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef
- Date: 2015
- Type: Text , Conference paper
- Relation: 25th European Safety and Reliability Conference, ESREL 2015; Zurich, Switzerland; 7th-10th September 2015 p. 2229-2234
- Full Text: false
- Reviewed:
- Description: Nowadays, improving system reliability is becoming an important criterion for engineering industries. Many studies have been developed to evaluate the reliability of the systems which is the first step in system improvement. Most of these studies have been done in non-dynamic conditions in which the components have the constant reliability values during functioning periods. However, the components' reliability level varies over time due to both failures and maintenance actions. Therefore, time dimension should be added into system reliability evaluation. In this paper, a dynamic assessment is presented for multi-state weighted k-out-of-n systems. The k-out-of-n system is a popular structure in fault-tolerant systems in which n components work in parallel form with a pre-defined k as a condition. This dynamic assessment considers the reliability variation of the components over finite and discrete time periods. It provides an opportunity to assign decision variables for each functioning period, and analyze the impact of each decision on the whole system reliability. In addition, the income generated during each period is defined as an importance weight of the components. Therefore, the present value of the system is obtained by Universal Generating Function (UGF) and engineering economics' tools. Furthermore, an optimization model is developed to find optimal decisions based on system reliability and cost. Since the system reliability is estimated by money, the expected profit of the system can be as the objective function. As a result, the objective function can maximize system reliability and minimize system cost simultaneously. A Matlab programming is created for a numerical example to illustrate the proposed model. © 2015 Taylor & Francis Group, London.
A bio-inspired computational language for kinesin nanomotor
- Authors: Khataee, H. , Ibrahim, Yousef
- Date: 2012
- Type: Text , Conference proceedings
- Relation: Industrial Technology (ICIT), 2012 IEEE International Conference, Athens, Greece, 19-21 March 2012
- Full Text: false
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- Description: Kinesin nanomotor is a tiny vehicle that transports molecular cargoes within the cells. Many kinesin nanomotors can attach to a single cargo and coordinate their behaviors to transport the cargo. This behavioral coordination of kinesin nanomotors can be defined through a communicational language that kinesin nanomotors follow to transport the cargo. This paper proposes a computational language for kinesin nanomotor which is inspired by the nanomotor's natural behavior. In this technique, we have used behavioral Deterministic Finite Automaton (DFA) model of kinesin nanomotor which indicated internal intelligent and autonomous decision-making process of the nanomotor in response to its cell. In addition, the behavioral responses of kinesin nanomotor to its cell, behavioral DFA model of the nanomotor, were mapped to a computational regular language for the nanomotor. The proposed computational language for kinesin nanomotor was acceptable by the behavioral DFA model and also in good agreement with the natural behavior of the nanomotor. The development of such computational languages among intelligent and autonomous nanoparticles in nature paves the way for constructing potential bio-inspired nanorobotic systems as well as designing of some computational languages for their controlling.
A new method of electrical equipment maintenance optimisation based on reliability analysis: industrial perspective
- Authors: DeLa Rosa, Wolman , Ibrahim, Yousef
- Date: 2008
- Type: Text , Conference paper
- Relation: Industrial Electronics, 2008. ISIE 2008. IEEE International Symposium p. 1796-1801
- Full Text: false
- Reviewed:
- Description: This paper describes a new methodology for developing common maintenance strategy based on reliability-centered maintenance (RCM) principles. The development took place in a major industrial establishment in South America. The name of this industrial establishment is suppressed for commercial confidentiality. Performance-based maintenance contract has become a general trend in many industrial organizations. This allows the organizations to focus on their core business while others handle maintenance tasks. This paper demonstrates that the transition of a maintenance contract based on body shop to a one based on performance is feasible. As demonstrated in the paper, this can be accomplished by changing the maintenance strategy from being based on vendor recommendations to a strategy based on RCM principles. The new strategy can computer-simulated to calculate the maintenance indicators. The produced indicators are the basis to change the traditional maintenance contract to a performance based maintenance contract. The experience gained and the method of simulation is explained in this paper. The optimization process and its results are discussed.
A new methodology of mobile robot navigation : The agoraphilic algorithm
- Authors: McFetridge, Lachlan , Ibrahim, Yousef
- Date: 2009
- Type: Text , Journal article
- Relation: Robotics and Computer-Integrated Manufacturing Vol. 25, no. 3 (2009 2009), p. 545-551
- Full Text: false
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- Description: The Agoraphilic algorithm is an optimistic approach to reactive path planning for mobile robot platforms. The technique uses virtual, attractive forces derived from the surrounding free space. Fuzzy logic is utilised to limit the ‘free-space’ force so as to promote the movement towards the goal. The algorithm was designed to be a robust technique for reactive navigation that could be implemented without the fuss of tuning the sensitive parameters required for other classical navigation routines. Several simulations plus some preliminary experimental results are presented here to demonstrate the algorithm's potential.
A value-driven approach for optimizing reliability-redundancy allocation problem in multi-state weighted k-out-of-n system
- Authors: Khorshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef
- Date: 2016
- Type: Text , Journal article
- Relation: Journal of Manufacturing Systems Vol. 40, no. (2016), p. 54-62
- Full Text: false
- Reviewed:
- Description: This study concentrates on optimizing a multi-state weighted k-out-of-n system consisting of different types of reparable components. An optimization model is developed to decide upon both optimal redundancy allocation and best maintenance activities for reliability allocation. The optimization model is to maximize system reliability and minimize system cost simultaneously. To reach this goal, a financial view has been employed to estimate the system reliability, and combine it with system cost. The proposed model determines the number of each component type in the system, and the maintenance actions and the time at which they should be applied. Also, the model is programmed by MATLAB, and Genetic Algorithm is used to solve a practical case. (C) 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Agoraphilic navigation algorithm in dynamic environment with obstacles motion tracking and prediction
- Authors: Hewawasam, Hasitha , Ibrahim, Yousef , Kahandawa, Gayan , Choudhury, Tanveer
- Date: 2022
- Type: Text , Journal article
- Relation: Robotica Vol. 40, no. 2 (2022), p. 329-347
- Full Text: false
- Reviewed:
- Description: This paper presents a new algorithm to navigate robots in dynamically cluttered environments. The proposed algorithm uses basic concepts of space attraction (hence the term Agoraphilic) to navigate robots through dynamic obstacles. The new algorithm in this paper is an advanced development of the original Agoraphilic navigation algorithm that was only able to navigate robots in static environments. The Agoraphilic algorithm does not look for obstacles (problems) to avoid but rather for a free space (solutions) to follow. Therefore, it is also described as an optimistic navigation algorithm. This algorithm uses only one attractive force created by the available free space. The free-space concept allows the Agoraphilic algorithm to overcome inherited challenges of general navigation algorithms. However, the original Agoraphilic algorithm has the limitation in navigating robots only in static, not in dynamic environments. The presented algorithm was developed to address this limitation of the original Agoraphilic algorithm. The new algorithm uses a developed object tracking module to identify the time-varying free spaces by tracking moving obstacles. The capacity of the algorithm was further strengthened by the new prediction module. Future space prediction allowed the algorithm to make decisions considering future growing/diminishing free spaces. This paper also includes a bench-marking study of the new algorithm compared with a recently published APF-based algorithm under a similar operating environment. Furthermore, the algorithm was validated based on experimental tests and simulation tests. © 2022 Cambridge University Press. All rights reserved.
Agoraphilic navigation algorithm under dynamic environment
- Authors: Hewawasam, Hasitha , Ibrahim, Yousef , Appuhamillage, Gayan , Choudhury, Tanveer
- Date: 2022
- Type: Text , Journal article
- Relation: IEEE/ASME Transactions on Mechatronics Vol. 27, no. 3 (2022), p. 1727-1737
- Full Text: false
- Reviewed:
- Description: This article presents a summary of the work done on the development of a new algorithm for mobile robot navigation in unknown dynamic environment. The developed humanlike algorithm uses a free-space attraction (Agoraphilic) concept for robot navigation. The algorithm presented in this article is an advanced development of the Agoraphilic navigation algorithm. The Agoraphilic algorithm does not look for obstacles (problems) to avoid but rather for free spaces toward the goal (solutions) to follow. The original Agoraphilic while it was able to overcome the limitations of the traditional algorithms had its own limitations in navigating robots in environments cluttered with moving obstacles. The new Agoraphilic Navigation Algorithm under Dynamic Environment (ANADE) was developed to overcome those limitations. ANADE consists of seven main modules reported in this article. The objects tracking and objects prediction methodologies developed for the algorithm estimate future growing free-space passages toward the goal. The algorithm generates a time-varying single attractive force to pull the robot through the free space toward the predicted (future) growing free-space passages leading to the goal. The new algorithm was tested, not only through simulation, but also through experimental work. Summary of the experimental results is presented and discussed in this article. © 1996-2012 IEEE.
An optimization model for multi-state weighted kout-of-n system reliability value
- Authors: Korshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef
- Date: 2013
- Type: Text , Conference proceedings
- Relation: IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria Nov. 2013, p.4357-4361
- Full Text: false
- Reviewed:
- Description: A reliability optimization model is proposed in this paper for multi-state weighted k-out-of-n systems. In this model, income generated by components through each functioning period is used as a reliability index. Therefore, time value of money is used in the presented optimization model to estimate both system's reliability and cost. The system reliability is evaluated by Universal Generating Function (UGF). The model's objective function is to maximize the net present value (NPV) of the system. Therefore, it would maximize the system reliability and minimize the system cost simultaneously. A numerical example is presented in this paper to illustrate the model by finding the optimal design of the system, and the best time for maintenance plan. Also, a discussion is provided based on the result.
An unreliability analysis for k-out-of-n: F system
- Authors: Ibrahim, Yousef , Gunawan, Indra , Khorshidi, Hadi
- Date: 2014
- Type: Text , Conference paper
- Relation: Proceedings of 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM 2014): Advanced Reliability and Maintenance Modeling VI p. 208-215
- Full Text: false
- Reviewed:
Applying UGF Concept to Enhance the Assessment Capability of FMEA
- Authors: Khorshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef
- Date: 2016
- Type: Text , Journal article
- Relation: Quality and Reliability Engineering International Vol. 32, no. 3 (Apr 2016), p. 1085-1093
- Full Text: false
- Reviewed:
- Description: The purpose of this paper is to propose a modified version of Failure Mode and Effects Analysis (FMEA) to alleviate its drawbacks. FMEA is an important tool in risk evaluation and finding the priority of potential failure modes for corrective actions. In the proposed method, the Universal Generating Function (UGF) approach has been used to improve the assessment capability of the conventional Risk Priority Number (RPN) in ranking. The new method is named as URPN. It generates the most number of unique values in comparison with the previous methods and considers relative importance for the parameters while it is easy to compute. More unique numbers help to avoid from having the same priority level for different failure modes which represent various risk levels. A case study has been employed to demonstrate that the URPN not only can improve the shortcomings but also is able to provide accurate values for risk assessment. Copyright (c) 2015 John Wiley & Sons, Ltd.
Comparative study on object tracking algorithms for mobile robot navigation in GPS-denied environment
- Authors: Hewawasam, Hasitha , Ibrahim, Yousef , Kahandawa, Gayan , Choudhury, Tanveer
- Date: 2019
- Type: Text , Conference proceedings
- Relation: 2019 IEEE International Conference on Industrial Technology, ICIT 2019; Melbourne, Australia; 13th-15th February 2019 Vol. 2019-February, p. 19-26
- Full Text: false
- Reviewed:
- Description: This paper presents a comparative study conducted on the performance of the commonly used object tracking and location prediction algorithms for mobile robot navigation in a dynamically cluttered and GPS-denied mining environment. The study was done to test the different algorithms for the same set criteria (such as accuracy and computational time) under the same conditions.The identified commonly used algorithms for object tracking and location prediction of moving objects used in this investigation are Kalman filter (KF), extended Kalman filter (EKF) and particle filter (PF). The study results of those algorithms are analyzed and discussed in this paper. A trade-off was apparent. However, in overall performance KF has shown its competitiveness.The result from the study has found that the KF based algorithm provides better performance in terms of accuracy in tracking dynamic objects under commonly used benchmarks. This finding can be used in development of an efficient robot navigation algorithm.
- Description: Proceedings of the IEEE International Conference on Industrial Technology
Computing optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms
- Authors: Khataee, H. , Ibrahim, Yousef , Sourchi, S. , Eskandari, L. , Teh Noranis, M.
- Date: 2012
- Type: Text , Journal article
- Relation: COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 31, no. 2 (2012), p. 387-400
- Full Text: false
- Reviewed:
- Description: Purpose – One of the significant underlying principles of nanorobotic systems deals with the understanding and conceptualization of their respective complex nanocomponents. This paper introduces a new methodology to compute a set of optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms based on dynamic programming and greedy algorithm. Design/methodology/approach – Buckyball, C60, is composed of sixty equivalent carbon atoms arranged as a highly symmetric hollow spherical cage in the form of a soccer ball. At first, Wiener, hyper-Wiener, Harary and reciprocal Wiener indices were computed using dynamic programming and presented them as: W(Buckyball)=11870.4, WW(Buckyball)=52570.9, Ha(Buckyball)=102.2 and RW(Buckyball)=346.9. The polynomials of Buckyball, Hosoya and hyper-Hosoya, which are in relationship with Buckyball's indices, have also been computed. The relationships between Buckyball's indices and polynomials were then computed and demonstrated a good agreement with their mathematical equations. Also, a graph algorithm based on greedy algorithms was used to find some optimal electronic aspects of Buckyball's structure by computing the Minimum Weight Spanning Tree (MWST) of Buckyball. Findings – The computed MWST was indicated that for connecting sixty carbon atoms of Buckyball together: the minimum numbers of double bonds were 30; the minimum numbers of single bonds were 29; and the minimum numbers of electrons were 178. These results also had good agreement with the principles of the authors' used greedy algorithm. Originality/value – This paper has used the graph algorithms for computing the optimal electronic and mathematical properties of BB. It has focused on mathematical properties of BB including Wiener, hyper-Wiener, Harary and reciprocal Wiener indices as well as Hosoya and Hyper-Hosoya polynomials and computerized them with dynamic programming graph algorithms.
Cyclic production for robotic cells served by multi-function robots with resumable processing regime
- Authors: Foumani, Mehdi , Ibrahim, Yousef , Gunawan, Indra
- Date: 2013
- Type: Text , Conference paper
- Relation: 2013 IEEE International Conference on Industrial Engineering and Engineering Management, Bangkok, (10 - 13 December 2013) p. 551-555
- Full Text: false
- Reviewed:
- Description: This paper addresses the problem of finding the optimal robot move cycle to minimise the cycle time of two-machine cells. The earlier robot's function was mainly moving parts between machines in a manufacturing process. We lift this assumption on robot tasks and assumed a special robot, namely multi-function, which performs a unique operation in transit. This robot starts performing this operation after unloading a part from input buffer and finishes it before loading the part to the output buffer. The processing mode on robot is “stop resume”. Thus, regardless of the gap interrupts during the operation, the robot continues processing on part when it is reloaded to the robot without any loss in time. The focus of this study is on one-unit cycles since they are very popular in industry. The cycle time of two possible one-unit cycles is obtained, and the optimality condition of them is determined.
Cyclic scheduling in small-scale robotic cells served by a multi-function robot
- Authors: Foumani, Mehdi , Ibrahim, Yousef , Gunawan, Indra
- Date: 2013
- Type: Text , Conference proceedings
- Relation: IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Nov. 2013, Vienna, Austria pp.4362-4367
- Full Text: false
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- Description: The industrial robot is one of the popular devices used in fully automatic production lines as material handling tool. A consequential problem is finding a cyclic robot movement which gives the maximum cell output in mass production environments. The Robotic Cell Scheduling Problem (RCSP) is predominantly separated into two different problems: Single-Function Robotic Cell (SFRC) and Multi-Function Robotic Cell (MFRC) scheduling problem. These problems are layout-oriented and operation-oriented, respectively. Literature concerning with former case considered a robotic system served by a transporting robot performing a single task. This kind of transporting robot is usually called Single-Function Robot (SFR). For the latter case, the robotic system served by a Multi-Function Robot (MFR) which simultaneously perform an arbitrary task in addition to parts transportation task. Giving a real-life example of MFRs, the use of a class of grippers performing in-process control is significantly increased in industry. The grippers, install at the end of MFR arm, can perform quality control tasks (e.g. accurately measure diameters) while part is carried to next machine. Figure 1 shows an example of these grippers used for measuring the diameter of crankshaft [1]. The measuring heads are integrated into the automation by adding gages and crankshaft locating features to MFR using in these lines. Also, there is a special kind of MFR, namely SDA10, which is suitable for assembly and part transfer in production lines especially if fixturing is costly [2]. Thus, it is crucial to undertake a comprehensive research onto effect of MFRs on production rate.
Development and bench-marking of agoraphilic navigation algorithm in dynamic environment
- Authors: Hewawasam, Hasitha , Ibrahim, Yousef , Kahandawa, Gayan , Choudhury, Tanveer , IEEE
- Date: 2019
- Type: Text , Book chapter
- Relation: 2019 IEEE 28th International Symposium on Industrial Electronics p. 1156-1161
- Full Text: false
- Reviewed:
- Description: This paper presents a summary of research which was conducted in developing a new human-like navigation methodology based on the Agoraphilic algorithm. This new methodology is capable of maneuvering robots in both static and dynamically clutter unknown environments. The Agoraphilic algorithm is an "optimistic" navigation algorithm. The algorithm is based on free space attraction rather than repulsion of obstacles for navigation. Therefore, this algorithm directs robots to follow the free space leading to the goal instead of avoiding obstacles. This approach has eliminated many draw backs of the traditional APF algorithm. However, the major limitation of the previously developed Agoraphilic algorithm could only deal with static environment. The new proposed algorithm has successfully extended the capacity of Agoraphilic algorithm to deal with environment cluttered with dynamic obstacles. The new Agoraphilic algorithm uses a tracking and prediction methodology to estimate the path of unknown moving objects. The estimated locations of the moving objects are combined with static object locations in the robot's visible region to generate time-varying free space attractive forces. These time varying forces maneuver the robot to the goal in dynamically cluttered unknown environment without collusions. To demonstrate the algorithm's ability, several simulations were performed. Furthermore, the new algorithm was tested and bench-marked against other APF published work under similar environment and conditions. The comparative results are discussed and showed the effectiveness of the new Algoraphilic navigation algorithm.
Development of a spherical parallel manipulator as a haptic device for a tele-operation system: Application to robotic surgery
- Authors: Saafi, Hadi , Laribi, Med Amine , Zeghoul, Said , Ibrahim, Yousef
- Date: 2013
- Type: Text , Conference proceedings
- Relation: IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Nov. 2013, Vienna, Austria p. 4097-4102
- Full Text: false
- Reviewed:
- Description: In tele-operation applications, especially in surgery, haptic devices need to exhibit a high degree of rigidity and accuracy. This paper deals with the development of a spherical parallel manipulator (SPM) that enables the satisfaction of those characteristics. The parallel architecture enables the use of this kind of robot as master in a tele-operation system. Moreover, the SPM has a center of rotation that makes it a natural candidate and more adapted to minimally invasive surgery application. However, the parallel manipulator presents a poor behavior in singular configuration. In this paper we discuss the technique we used to overcome the singularity effects. We also present the methodology of using additional sensor to avoid kinematic structure problem without design changes. The investigation of the developed solution is detailed in this paper. Also, the experimental results of the newly developed haptic device are presented in this paper.
Development of flexible haptic forceps based on the electrohydraulic transmission system
- Authors: Ogawa, Kenji , Ibrahim, Yousef , Ohnishi, Kouhei
- Date: 2018
- Type: Text , Journal article
- Relation: IEEE Transactions on Industrial Informatics Vol. 14, no. 12 (2018), p. 5256-5267
- Full Text: false
- Reviewed:
- Description: Minimally invasive surgery (MIS) has many benefits, e.g., unnecessary trauma and blood loss can be minimized by opening tiny surgery scars, recovery process of patients can be lessened, and the possibilities of complications can be decreased. The natural orifice transluminal surgery (NOTES) is one of the MIS surgical methodologies. NOTES surgery is performed using an endoscope. This methodology does not rely on making holes to patients' body to insert the medical instruments. Although some medical robots for NOTES have been proposed, current robots mainly suffer from the absence/limitation of haptic feedback to the surgeon's hands. In order to overcome this problem, this paper proposes electro hydraulic transmission system (EHTS) based forceps. The EHTS is a remote actuation system using fluid energy. By using the EHTS, the classical position and force transmission losses will not be influenced by the tube's shape. The validity of the proposal and its advantages have been experimentally verified and presented in this paper.
Development of flexible haptic forceps based on the electrohydraulic transmission system
- Authors: Ogawa, Kenji , Ibrahim, Yousef , Ohnishi, Kouhei
- Date: 2018
- Type: Text , Journal article
- Relation: IEEE Transactions on Industrial Informatics Vol. 14, no. 12 (2018), p. 5256-5267
- Full Text: false
- Reviewed:
- Description: Minimally invasive surgery (MIS) has many benefits, e.g., unnecessary trauma and blood loss can be minimized by opening tiny surgery scars, recovery process of patients can be lessened, and the possibilities of complications can be decreased. The natural orifice transluminal surgery (NOTES) is one of the MIS surgical methodologies. NOTES surgery is performed using an endoscope. This methodology does not rely on making holes to patients' body to insert the medical instruments. Although some medical robots for NOTES have been proposed, current robots mainly suffer from the absence/limitation of haptic feedback to the surgeon's hands. In order to overcome this problem, this paper proposes electro hydraulic transmission system (EHTS) based forceps. The EHTS is a remote actuation system using fluid energy. By using the EHTS, the classical position and force transmission losses will not be influenced by the tube's shape. The validity of the proposal and its advantages have been experimentally verified and presented in this paper.
E-Learning in Industrial Electronics during Covid-19
- Authors: Dunai, Larisa , Martins, Joao , Umetani, Kazuhiro , Lucia, Oscar , Ibrahim, Yousef , Appuhamillage, G. K.
- Date: 2021
- Type: Text , Conference paper
- Relation: 22nd IEEE International Conference on Industrial Technology, ICIT 2021 Vol. 2021-March, p. 1227-1233
- Full Text: false
- Reviewed:
- Description: The educational methodologies employed in Industrial Electronics have been affected by Covid-19. In many cases, conventional learning methods relying on face-to-face lectures have been replaced by online methodologies. The whole process has required a fast adaptation and development of the e-learning tools to ensure a quality of theoretical, practical and laboratory lectures, as well as the development of new methods for the reliable assessment of the learning process. From this perspective, the present paper deals with the different strategies that have been implemented in institutions of several countries located in different geographical areas, including Portugal, Spain, Japan and Australia. It is shown that the use of methodologies, such as flip teaching, has provided a wide variety of possibilities to adapt to the new educational context. Moreover, for Industrial Electronics degrees, the use of virtual or remote laboratories, portable learning tools and advanced information and communication technologies have also risen as valuable resources. The paper also reports the problems arising during the development of the e-learning tools, their implementation constraints, and the evaluation of their results. © 2021 IEEE.
e-teaching and e-learning in engineering course design
- Authors: Ibrahim, Yousef , Brack, Charlotte
- Date: 2009
- Type: Text , Conference proceedings
- Full Text: false
- Description: This paper examines the inputs of two different processes and the linkage between those processes. The processes examined in this paper are e-Teaching and e-Learning. Many conferences and journals are devoted to publishing on e-learning while in most cases they address the issues of e-teaching, which is a different process. In recent years Universities around the world are competing to take advantage of the e-learning benefits including its economic incentives. Furthermore, many academic institutions have embraced the e-learning philosophy until it became the objective. This phenomenon has motivated the authors to conduct a study to thoroughly examine e-learning as part of the overall learning process. In this paper the authors reflect on their experience in e-teaching/e-learning attempting to make the distinction clearer and define the relationship.