Search results for: Cost Variance

Authors: Ian Kree, Davina Chin Lee Yien

Abstract:

This paper presents Cost per Equivalent Wafer Out, which we find useful in wafer fab operational cost monitoring and controlling. It removes the loading and product mix effect in the cost variance analysis. The operation heads, therefore, could immediately focus on identifying areas for cost improvement. Without this, they would have to measure the impact of the loading variance and product mix variance between actual and budgeted prior to make any decision on cost improvement. Cost per Equivalent Wafer Out, thereby, increases efficiency in wafer fab operational cost monitoring and controlling.

Keywords: Cost Control, Cost Variance, Operational Expenditure, Semiconductor.

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Authors: Mahmood M. Al-Imam, M. Mustafa

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In this paper, we present an experimental testing for a new algorithm that determines an optimal controller-s coefficients for output variance reduction related to Linear Time Invariant (LTI) Systems. The algorithm features simplicity in calculation, generalization to minimal and non-minimal phase systems, and could be configured to achieve reference tracking as well as variance reduction after compromising with the output variance. An experiment of DCmotor velocity control demonstrates the application of this new algorithm in designing the controller. The results show that the controller achieves minimum variance and reference tracking for a preset velocity reference relying on an identified model of the motor.

Keywords: Output variance, minimum variance, overparameterization, DC-Motor.

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Authors: Alireza Azimi Sani

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This paper discusses the design characteristics management accounting systems should have to be useful for strategic planning and control and provides brief introductions to strategic variance analysis, profit-linked performance measurement models and balanced scorecard. It shows two multi-period, multiproduct models are specified, can be related to Porter's strategy framework and cost and revenue drivers, and can be used to support strategic planning, control and cost management.

Keywords: Accounting, balanced scorecard, profit-linked, strategic management, variance analysis.

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Authors: Erna T. Herdiani, Maman A. Djauhari

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In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector variance. Its sampling distribution will be investigated to make its applications possible.

Keywords: Asymptotic distribution, covariance matrix, likelihood ratio test, vector variance.

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Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

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Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: Variance, lower semi-variance, range-based volatility.

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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Authors: Cuong Nguyen Khac, Ju H. Park, Ho-Youl Jung

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This paper proposes a new approach to perform the problem of real-time face detection. The proposed method combines primitive Haar-Like feature and variance value to construct a new feature, so-called Variance based Haar-Like feature. Face in image can be represented with a small quantity of features using this new feature. We used SVM instead of AdaBoost for training and classification. We made a database containing 5,000 face samples and 10,000 non-face samples extracted from real images for learning purposed. The 5,000 face samples contain many images which have many differences of light conditions. And experiments showed that face detection system using Variance based Haar-Like feature and SVM can be much more efficient than face detection system using primitive Haar-Like feature and AdaBoost. We tested our method on two Face databases and one Non-Face database. We have obtained 96.17% of correct detection rate on YaleB face database, which is higher 4.21% than that of using primitive Haar-Like feature and AdaBoost.

Keywords: AdaBoost, Haar-Like feature, SVM, variance, Variance based Haar-Like feature.

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Authors: H. B. Kekre, Kavita Patil

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This paper describes a novel and effective approach to content-based image retrieval (CBIR) that represents each image in the database by a vector of feature values called “Standard deviation of mean vectors of color distribution of rows and columns of images for CBIR". In many areas of commerce, government, academia, and hospitals, large collections of digital images are being created. This paper describes the approach that uses contents as feature vector for retrieval of similar images. There are several classes of features that are used to specify queries: colour, texture, shape, spatial layout. Colour features are often easily obtained directly from the pixel intensities. In this paper feature extraction is done for the texture descriptor that is 'variance' and 'Variance of Variances'. First standard deviation of each row and column mean is calculated for R, G, and B planes. These six values are obtained for one image which acts as a feature vector. Secondly we calculate variance of the row and column of R, G and B planes of an image. Then six standard deviations of these variance sequences are calculated to form a feature vector of dimension six. We applied our approach to a database of 300 BMP images. We have determined the capability of automatic indexing by analyzing image content: color and texture as features and by applying a similarity measure Euclidean distance.

Keywords: Standard deviation Image retrieval, color distribution, Variance, Variance of Variance, Euclidean distance.

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Authors: Reza Lotfalian, Sudarshan Martins, Peter Radziszewski

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The effect of reliability on life-cycle cost, including initial and maintenance cost of a system is studied. The failure probability of a component is used to calculate the average maintenance cost during the operation cycle of the component. The standard deviation of the life-cycle cost is also calculated as an error measure for the average life-cycle cost. As a numerical example, the model is used to study the average life-cycle cost of an electric motor.

Keywords: Initial Cost, Life-cycle cost, Maintenance Cost, Reliability.

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Authors: Johnson Adafin, James O. B. Rotimi, Suzanne Wilkinson, Abimbola O. Windapo

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An aspect of client expenditure management that requires attention is the level of accuracy achievable in design-stage elemental cost planning. This has been a major concern for construction clients and practitioners in New Zealand (NZ). Pre-tender estimating inaccuracies are significantly influenced by the level of risk information available to estimators. Proper cost planning activities should ensure the production of a project’s likely construction costs (initial and final), and subsequent cost control activities should prevent unpleasant consequences of cost overruns, disputes and project abandonment. If risks were properly identified and priced at the design stage, observed variance between design-stage elemental cost plans (ECPs) and final tender sums (FTS) (initial contract sums) could be reduced. This study investigates the variations between design-stage ECPs and FTS of construction projects, with a view to identifying risk factors that are responsible for the observed variance. Data were sourced through interviews, and risk factors were identified by using thematic analysis. Access was obtained to project files from the records of study participants (consultant quantity surveyors), and document analysis was employed in complementing the responses from the interviews. Study findings revealed the discrepancies between ECPs and FTS in the region of -14% and +16%. It is opined in this study that the identified risk factors were responsible for the variability observed. The values obtained from the analysis would enable greater accuracy in the forecast of FTS by Quantity Surveyors. Further, whilst inherent risks in construction project developments are observed globally, these findings have important ramifications for construction projects by expanding existing knowledge on what is needed for reasonable budgetary performance and successful delivery of construction projects. The findings contribute significantly to the study by providing quantitative confirmation to justify the theoretical conclusions generated in the literature from around the world. This therefore adds to and consolidates existing knowledge.

Keywords: Accuracy, design-stage, elemental cost plan, final tender sum, New Zealand.

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Authors: Zeinab Ghasemi, S. Amirhassan Monadjemi, Abbas Vafaei

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This paper presents a comparative analysis of a new unsupervised PCA-based technique for steel plates texture segmentation towards defect detection. The proposed scheme called Variance Based Component Analysis or VBCA employs PCA for feature extraction, applies a feature reduction algorithm based on variance of eigenpictures and classifies the pixels as defective and normal. While the classic PCA uses a clusterer like Kmeans for pixel clustering, VBCA employs thresholding and some post processing operations to label pixels as defective and normal. The experimental results show that proposed algorithm called VBCA is 12.46% more accurate and 78.85% faster than the classic PCA.

Keywords: Principal Component Analysis; Variance Based Component Analysis; Defect Detection; Texture Segmentation.

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Authors: M. R. Bhuiyan, S. M. M. Hossain, M. Z. Islam

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Autism Spectrum Disorder (ASD) is the fastest growing serious developmental disorder characterized by social deficits, communicative difficulties, and repetitive behaviors. ASD is an emerging public health issue globally which is associated with huge financial burden to the family, community and the nation. The aim of this study was to assess the financial burden of family for the children with Autism spectrum Disorder. This cross-sectional study was carried out from July 2015 to June 2016 among 154 children with ASD to assess the financial burden of family. Data were collected by face-to-face interview with semi-structured questionnaire following systematic random sampling technique. Majority (73.4%) children were male and mean (±SD) age was 6.66 ± 2.97 years. Most (88.8%) of the children were from urban areas with average monthly family income Tk. 41785.71±23936.45. Average monthly direct cost of the children was Tk.17656.49 ± 9984.35, while indirect cost was Tk. 13462.90 ± 9713.54 and total treatment cost was Tk. 23076.62 ± 15341.09. Special education cost (Tk. 4871.00), cost of therapy (Tk. 4124.07) and travel cost (Tk. 3988.31) were the major types of direct cost, while loss of income (Tk.14570.18) was the chief indirect cost incurred by the families. The study found that majority (59.8%) of the children attended special schools were incurred Tk.20001-78700 as total treatment cost, which were statistically significant (p<0.001). Again, families with higher monthly family income incurred higher treatment cost (r=0.526, p<0.05). Difference between mean direct and indirect cost was found significant (t=4.190, df=61, p<0.001). According to the analysis of variance, mean difference of father’s educational status among direct cost (F=10.337, p<0.001) and total treatment cost (F=7.841, p<0.001), which were statistically significant. The study revealed that maximum children with ASD were under five years, three-fourth were male. According to monthly family income, maximum family were in middle class. The study recommends cost effective interventions and financial safety-net measures to reduce the financial burden of families for the children with ASD.

Keywords: Autism spectrum disorder, financial burden, direct cost, indirect cost, Special education.

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: Noise, signal-to-noise ratio, stochastic signals, variance estimation.

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Authors: Remzi Saltoglu, Nazmia Humaira, Gokhan Inalhan

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During aircraft maintenance scheduling, operator calculates the budget of the maintenance. Usually, this calculation includes only the costs that are directly related to the maintenance process such as cost of labor, material, and equipment. In some cases, overhead cost is also included. However, in some of those, downtime cost is neglected claiming that grounding is a natural fact of maintenance; therefore, it is not considered as part of the analytical decision-making process. Based on the normalized data, we introduce downtime cost with its monetary value and add its seasonal character. We envision that the rest of the model, which works together with the downtime cost, could be checked with the real life cases, through the review of MRO cost and airline spending in the particular and scheduled maintenance events.

Keywords: Aircraft maintenance, downtime, downtime cost, maintenance cost.

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Authors: Kalu Ram Meena, Aditi Kar Gangopadhyay, Satrajit Mandal

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Two normal populations with different means and same variance are considered, where the variance is known. The population with the smaller sample mean is selected. Various estimators are constructed for the mean of the selected normal population. Finally, they are compared with respect to the bias and MSE risks by the mehod of Monte-Carlo simulation and their performances are analysed with the help of graphs.

Keywords: Estimation after selection, Brewster-Zidek technique.

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Authors: Larisa N. Pop, Irina M. Ban

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This paper aims to present the main instruments used in the economic literature for measuring the price risk, pointing out on the advantages brought by the conditional variance in this respect. The theoretical approach will be exemplified by elaborating an EGARCH model for the price returns of wheat, both on Romanian and on international market. To our knowledge, no previous empirical research, either on price risk measurement for the Romanian markets or studies that use the ARIMA-EGARCH methodology, have been conducted. After estimating the corresponding models, the paper will compare the estimated conditional variance on the two markets.

Keywords: conditional variance, GARCH models, price risk, volatility

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Authors: Nurul Zahirah M.A., N. Zainul Abidin

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Green buildings have been commonly cited to be more expensive than conventional buildings. However, limited research has been conducted to clearly identify elements that contribute to this cost differential. The construction cost of buildings can be typically divided into “hard" costs and “soft" cost elements. Using a review analysis of existing literature, the study identified six main elements in green buildings that contribute to the general cost elements that are “soft" in nature. The six elements found are insurance, developer-s experience, design cost, certification, commissioning and energy modeling. Out of the six elements, most literatures have highlighted the increase in design cost for green design as compared to conventional design due to additional architectural and engineering costs, eco-charettes, extra design time, and the further need for a green consultant. The study concluded that these elements of soft cost contribute to the green premium or cost differential of green buildings.

Keywords: Green building, cost differential, soft cost, intangible cost.

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Authors: Heung Jae Cho, Jae Il Park

Abstract:

This paper presents the development of an MODAPTS based cost estimating system to help designers in estimating the manufacturing cost of a assembly products which is belonged from the workers in working fields. Competitiveness of manufacturing cost is getting harder because of the development of Information and telecommunication, but also globalization. Therefore, the accuracy of the assembly cost estimation is getting important. DFA and MODAPTS is useful method for measuring the working hour. But these two methods are used just as a timetable. Therefore, in this paper, we suggest the process of measuring the working hours by MODAPTS which includes the working field-s accurate information. In addition, we adduce the estimation method of accuracy assembly cost with the real information. This research could be useful for designers that can estimate the assembly cost more accurately, and also effective for the companies that which are concerned to reduce the product cost.

Keywords: Cost estimation, DFA, MODAPTS, Assembly cost

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: Temporal differencing, video summarization, histogram differencing, sum conditional variance.

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Authors: Jaebum Park, Vladimir M. Zatsiorsky

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The performance results of the athletes competed in the 1988-2008 Olympic Games were analyzed (n = 166). The data were obtained from the IAAF official protocols. In the principal component analysis, the first three principal components explained 70% of the total variance. In the 1st principal component (with 43.1% of total variance explained) the largest factor loadings were for 100m (0.89), 400m (0.81), 110m hurdle run (0.76), and long jump (–0.72). This factor can be interpreted as the 'sprinting performance'. The loadings on the 2nd factor (15.3% of the total variance) presented a counter-intuitive throwing-jumping combination: the highest loadings were for throwing events (javelin throwing 0.76; shot put 0.74; and discus throwing 0.73) and also for jumping events (high jump 0.62; pole vaulting 0.58). On the 3rd factor (11.6% of total variance), the largest loading was for 1500 m running (0.88); all other loadings were below 0.4.

Keywords: Decathlon, principal component analysis, Olympic Games, multivariate statistical analysis.

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Authors: S. A. Mohamed, A. S. Zayed, O. A. Abolaeha

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A new Feed-Forward/Feedback Generalized Minimum Variance Pole-placement Controller to incorporate the robustness of classical pole-placement into the flexibility of generalized minimum variance self-tuning controller for Single-Input Single-Output (SISO) has been proposed in this paper. The design, which provides the user with an adaptive mechanism, which ensures that the closed loop poles are, located at their pre-specified positions. In addition, the controller design which has a feed-forward/feedback structure overcomes the certain limitations existing in similar poleplacement control designs whilst retaining the simplicity of adaptation mechanisms used in other designs. It tracks set-point changes with the desired speed of response, penalizes excessive control action, and can be applied to non-minimum phase systems. Besides, at steady state, the controller has the ability to regulate the constant load disturbance to zero. Example simulation results using both simulated and real plant models demonstrate the effectiveness of the proposed controller.

Keywords: Pole-placement, Minimum variance control, self-tuning control and feedforward control.

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained. 

Keywords: adaptive filtering, Bayesian approach Kalman filtering approach, variance tracking

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Authors: O. J. Olaniran, P. E. D. Love, D. J. Edwards, O. Olatunji, J. Matthews

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Cost overruns are a persistent problem in oil and gas megaprojects. Whilst the extant literature is filled with studies on incidents and causes of cost overruns, underlying theories to explain their emergence in oil and gas megaprojects are few. Yet, a way to contain the syndrome of cost overruns is to understand the bases of ‘how and why’ they occur. Such knowledge will also help to develop pragmatic techniques for better overall management of oil and gas megaprojects. The aim of this paper is to explain the development of cost overruns in hydrocarbon megaprojects through the perspective of chaos theory. The underlying principles of chaos theory and its implications for cost overruns are examined and practical recommendations proposed. In addition, directions for future research in this fertile area provided.

Keywords: Chaos theory, oil and gas, cost overruns, megaprojects.

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Authors: Nazirah Zainul Abidin, Nurul Zahirah Mokhtar Azizi

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Cost has always been the leading concern in green building development. The perception that construction cost for green building is higher than conventional buildings has only made the discussion of green building cost more difficult. Understanding the factors that will influence the cost of green construction is expected to shed light into what makes green construction more or at par with conventional projects, or perhaps, where cost can be optimised. This paper identifies the elements of cost before shifting the attention to the influencing factors. Findings from past studies uncovered various factors related to cost which are grouped into five focal themes i.e. awareness, knowledge, financial, technical, and government support. A conceptual framework is produced in a form of a flower diagram indicating the cost influencing factors of green building development. These factors were found to be both physical and non-physical aspects of a project. The framework provides ground for the next stage of research that is to further explore how these factors influence the project cost and decision making.

Keywords: Green project, factors influencing cost, hard cost, soft cost.

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Authors: Md. Ashikur Rahman Khan, M. M. Rahman

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In electrical discharge machining (EDM), a complete and clear theory has not yet been established. The developed theory (physical models) yields results far from reality due to the complexity of the physics. It is difficult to select proper parameter settings in order to achieve better EDM performance. However, modelling can solve this critical problem concerning the parameter settings. Therefore, the purpose of the present work is to develop mathematical model to predict performance characteristics of EDM on Ti-5Al-2.5Sn titanium alloy. Response surface method (RSM) and artificial neural network (ANN) are employed to develop the mathematical models. The developed models are verified through analysis of variance (ANOVA). The ANN models are trained, tested, and validated utilizing a set of data. It is found that the developed ANN and mathematical model can predict performance of EDM effectively. Thus, the model has found a precise tool that turns EDM process cost-effective and more efficient.

Keywords: Analysis of variance, artificial neural network, material removal rate, modelling, response surface method, surface finish.

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Authors: Ghada Karaki

Abstract:

The bridge vibration due to traffic loading has been a subject of extensive research during the last decades. A number of these studies are concerned with the effects of the unevenness of roadways on the dynamic responses of highway bridges. The road unevenness is often described as a random process that constitutes of different wavelengths. Thus, the study focuses on examining the effects of the random description of roadways on the dynamic response and its variance. A new setting of variance based sensitivity analysis is proposed and used to identify and quantify the contributions of the roadway-s wavelengths to the variance of the dynamic response. Furthermore, the effect of the vehicle-s speed on the dynamic response is studied.

Keywords: vehicle bridge interaction, sensitivity analysis, road unevenness, random processes, critical speeds

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Authors: Nurul Zahirah M.A., N. Zainul Abidin, Azlan Raofuddin Nuruddin

Abstract:

Despite all the hype about green building, many developers are still resistant to the idea of building green due to the common perception that green building construction is expensive. This contradicts with scholarly findings that identify only a marginal cost premium or none at all given that green design is considered during the design process and planning stage. Nevertheless, cost implications continue to become an issue when deciding to build green. The planning stage is of strategic importance as decisions made at this early stage would influence the project cost thereafter. Using analysis of existing literature, the paper identifies six elements of soft cost that are considered in the planning stage. The elements include consultants, green building consultant, certification, commissioning, market, and tax. Out of the six elements, commissioning represents the bulk of soft cost for buildings seeking green certification. The study concluded that, although hard cost may have a bigger impact on the project cost, but soft cost is the hidden cost which people tend to ignore. Poor consideration of soft cost during planning stage may lead to over-realistic expectations and ultimately, overlooked cost additions.

Keywords: Green building, cost element, soft cost, developer decision.

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Authors: A. Eman Mohammed

Abstract:

Algae-based fuel are considered a promising sources of clean energy, and because it has many advantages over traditional biofuel, research and business ventures have driven into developing and producing Algal-biofuel. But its production stages create a cost structure that it is not competitive with traditional fuels. Therefore, cost becomes the main obstacle in commercial production purpose. However, the present research which aims at using cost structure model, and designed MS-Dose program, to investigate the a mount of production cost and determined the parameter had great effect on it, second to measured the amount of contribution rate of algae in process the pollution by capturing Co2 from air . The result generated from the model shows that the production cost of biomass is between $0.137 /kg for 100 ha and $0.132 /kg for 500 ha which was less than cost of other studies, while gallon costs between $3.4 - 3.5, more than traditional sources of oil about $1 ,which regarded as a rate of contribution of algal in capturing CO2 from air.

Keywords: Cost Structure Model, Operation Costs(Production Cost), Capital Costs, Algae.

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Authors: Boukelkoul Lahcen

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The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: Cost, finite state, Markov model, operation, maintenance.

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