Search results for: moving least squares

Authors: W. Fethallah, L. Chraibi, N. Sefiani

Abstract:

The present paper is concerned with a statistical approach involving latent and manifest variables applied in order to assess the organization's social responsibility performance. The main idea is to develop an assessment tool and a measurement of the Social Responsibility Performance, enabling the company to characterize her performance regarding to the ISO 26000 standard's seven core subjects. For this, we conceptualize a structural equation modeling (SEM) which describes various causal connections between the Social Responsibility’s components. The SEM’s resolution is based on the Partial Least squares (PLS) method and the implementation is running in the XLSTAT software.

Keywords: Corporate social responsibility, latent and manifest variable, partial least squares, structural equation model.

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Authors: Mustafa Kisa, Fatih Mehmet Botsali

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Recent developments in automotive technology are focused on economy, comfort and safety. Vehicle tracking and collision detection systems are attracting attention of many investigators focused on safety of driving in the field of automotive mechatronics. In this paper, a vision-based vehicle detection system is presented. Developed system is intended to be used in collision detection and driver alert. The system uses RGB images captured by a camera in a car driven in the highway. Images captured by the moving camera are used to detect the moving vehicles in the image. A vehicle ahead of the camera is detected in daylight conditions. The proposed method detects moving vehicles by subtracting successive images. Plate height of the vehicle is determined by using a plate recognition algorithm. Distance of the moving object is calculated by using the plate height. After determination of the distance of the moving vehicle relative speed of the vehicle and Time-to-Collision are calculated by using distances measured in successive images. Results obtained in road tests are discussed in order to validate the use of the proposed method.

Keywords: Image possessing, vehicle tracking, license plate detection, computer vision.

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Authors: Jahanbakhsh Hamedi, Hassan Zohoor

Abstract:

This article proposes modeling, simulation and kinematic and workspace analysis of a spatial cable suspended robot as incompletely Restrained Positioning Mechanism (IRPM). These types of robots have six cables equal to the number of degrees of freedom. After modeling, the kinds of workspace are defined then an statically reachable combined workspace for different geometric structures of fixed and moving platform is obtained. This workspace is defined as the situations of reference point of the moving platform (center of mass) which under external forces such as weight and with ignorance of inertial effects, the moving platform should be in static equilibrium under conditions that length of all cables must not be exceeded from the maximum value and all of cables must be at tension (they must have non-negative tension forces). Then the effect of various parameters such as the size of moving platform, the size of fixed platform, geometric configuration of robots, magnitude of applied forces and moments to moving platform on workspace of these robots with different geometric configuration are investigated. Obtained results should be effective in employing these robots under different conditions of applied wrench for increasing the workspace volume.

Keywords: Kinematic modeling, applied wrench, workspace, cable based robot.

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Authors: S. N. Hosseini, S. M. H. Karimian

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A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.

Keywords: Immersed Boundary Method, conservation of mass and momentum laws, moving boundary, boundary condition.

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Authors: Deepthi Haridas, S Venkataraman, Geeta Varadan

Abstract:

Quasigroups are algebraic structures closely related to Latin squares which have many different applications. The construction of block cipher is based on quasigroup string transformation. This article describes a block cipher based Quasigroup of order 256, suitable for fast software encryption of messages written down in universal ASCII code. The novelty of this cipher lies on the fact that every time the cipher is invoked a new set of two randomly generated quasigroups are used which in turn is used to create a pair of quasigroup of dual operations. The cryptographic strength of the block cipher is examined by calculation of the xor-distribution tables. In this approach some algebraic operations allows quasigroups of huge order to be used without any requisite to be stored.

Keywords: quasigroups, latin squares, block cipher and quasigroup string transformations.

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Authors: Zaouche Mohamed, Amini Mohamed, Foughali Khaled, Aitkaid Souhila, Bouchiha Nihad Sarah

Abstract:

The aerodynamic coefficients are important in the evaluation of an aircraft performance and stability-control characteristics. These coefficients also can be used in the automatic flight control systems and mathematical model of flight simulator. The study of the aerodynamic aspect of flying systems is a reserved domain and inaccessible for the developers. Doing tests in a wind tunnel to extract aerodynamic forces and moments requires a specific and expensive means. Besides, the glaring lack of published documentation in this field of study makes the aerodynamic coefficients determination complicated. This work is devoted to the identification of an aerodynamic model, by using an aircraft in virtual simulated environment. We deal with the identification of the system, we present an environment framework based on Software In the Loop (SIL) methodology and we use Microsoft^TM Flight Simulator (FS-2004) as the environment for plane simulation. We propose The Total Least Squares Estimation technique (TLSE) to identify the aerodynamic parameters, which are unknown, variable, classified and used in the expression of the piloting law. In this paper, we define each aerodynamic coefficient as the mean of its numerical values. All other variations are considered as modeling uncertainties that will be compensated by the robustness of the piloting control.

Keywords: Aircraft aerodynamic model, Microsoft flight simulator, MQ-1 Predator, total least squares estimation, piloting the aircraft.

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Authors: Yongxin Yuan, Hao Liu

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In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

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Authors: Zeinab Galavani, Reza Rezaei-Nasirabad, Rasoul Sadighi-Bonabi

Abstract:

Using a force balanced translational-radial dynamics, phase space of the moving single bubble sonoluminescence (m- SBSL) in 85% wt sulfuric acid has been numerically calculated. This phase space is compared with that of single bubble sonoluminescence (SBSL) in pure water which has been calculated by using the mere radial dynamics. It is shown that in 85% wt sulfuric acid, in a general agreement with experiment, the bubble-s positional instability threshold lays under the shape instability threshold. At the onset of spatial instability of moving sonoluminescing (SL) bubble in 85% wt sulfuric acid, temporal effects of the hydrodynamic force on the bubble translational-radial dynamics have been investigated. The appearance of non-zero history force on the moving SL bubble is because of proper condition which was produced by high viscosity of acid. Around the moving bubble collapse due to the rapid contraction of the bubble wall, the inertial based added mass force overcomes the viscous based history force and induces acceleration on the bubble translational motion.

Keywords: Bjerknes force, History force, Reynolds number, Sonoluminescence.

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Authors: Osman Mohammed Hegazy, Ali Hamed El Bastawissy, Romani Farid Ibrahim

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In this paper, our concern is the management of mobile transactions in the shared area among many servers, when the mobile user moves from one cell to another in online partiallyreplicated distributed mobile database environment. We defined the concept of transaction and classified the different types of transactions. Based on this analysis, we propose an algorithm that handles the disconnection due to moving among sites.

Keywords: Concurrency, mobile database, transaction processing, two phase locking.

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Authors: ByungHoon Kang, Jeawook Shin, Ju-man Song, Hyun-Taek Choi, PooGyeon Park

Abstract:

In this study, we consider a special situation that only a pair of hydrophone on a moving underwater vehicle is available to localize a fixed acoustic source of far distance. The trigonometry can be used in this situation by using two different DOA of different locations. Notice that the distance between the two locations should be measured. Therefore, we assume that the vehicle is sailing straightly and the moving distance for each unit time is measured continuously. However, the accuracy of the localization using the trigonometry is highly dependent to the accuracy of DOAs and measured moving distances. Therefore, we proposed another method based on the extended Kalman filter that gives more robust and accurate localization result.

Keywords: Localization, acoustic, underwater, extended Kalman filter.

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Authors: Chunchom Pongchavalit

Abstract:

For the electrical metrics that describe photovoltaic cell performance are inherently multivariate in nature, use of a univariate, or one variable, statistical process control chart can have important limitations. Development of a comprehensive process control strategy is known to be significantly beneficial to reducing process variability that ultimately drives up the manufacturing cost photovoltaic cells. The multivariate moving average or MMA chart, is applied to the electrical metrics of photovoltaic cells to illustrate the improved sensitivity on process variability this method of control charting offers. The result show the ability of the MMA chart to expand to as any variables as needed, suggests an application with multiple photovoltaic electrical metrics being used in concert to determine the processes state of control.

Keywords: The multivariate moving average control chart, Photovoltaic processes control, Multivariate system.

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Authors: F. Z. Doğru, O. Arslan

Abstract:

In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. The simulation results show that the proposed robust estimators generally outperform the classical estimators in terms of bias and root mean square errors when there are outliers in data.

Keywords: Burr XII distribution, robust estimator, M-estimator, maximum likelihood, least squares.

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

Abstract:

In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: Elastic foundation, impact, moving load, thick plate.

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Authors: M. Jahanandish, Gh. Sadeghian, M. H. Daneshvar, M. H. Jahanandish

Abstract:

The amount of resistance of a particular medium like soil to the moving objects is the interest of many areas in science. These include soil mechanics, geotechnical engineering, powder mechanics etc. Knowledge of drag force is also used for estimating the amount of momentum of fired objects like bullets. This paper focuses on measurement of drag force of sand on a cone when it moves at a low constant speed. A 30-degree apex angle cone has been used for this purpose. The study consisted of both loose and dense conditions of the soil. The applied speed has been in the range of 0.1 to 10 mm/min. The results indicate that the required force is basically independent of the cone speed; but, it is very dependent on the material densification and confining stress.

Keywords: Drag force, sand, moving speed, friction angle, densification, confining stress.

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Authors: S. Elnobi, Iman El-Zahaby, Amr M. Mahros

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In mobile communication systems, performance and capacity are affected by multi-path fading, delay spread and Co-Channel Interference (CCI). For this reason Orthogonal Frequency Division Multiplexing (OFDM) and adaptive antenna array are used is required. The goal of the OFDM is to improve the system performance against Inter-Symbol Interference (ISI). An array of adaptive antennas has been employed to suppress CCI by spatial technique. To suppress CCI in OFDM systems two main schemes the pre-FFT and the post-FFT have been proposed. In this paper, through a system level simulation, the behavior of the pre-FFT and post-FFT beamformers for OFDM system has been investigated based on two algorithms namely, Least Mean Squares (LMS) and Recursive Least Squares (RLS). The performance of the system is also discussed in multipath fading channel system specified by 3GPP Long Term Evolution (LTE).

Keywords: OFDM, Beamforming, Adaptive Antennas Array.

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Authors: J.-H. Moon, D.-O Kim, R.-H. Park

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This paper presents a video matting method, which extracts the foreground and alpha matte from a video sequence. The objective of video matting is finding the foreground and compositing it with the background that is different from the one in the original image. By finding the motion vectors (MVs) using a sliced block matching algorithm (SBMA), we can extract moving regions from the video sequence under the assumption that the foreground is moving and the background is stationary. In practice, foreground areas are not moving through all frames in an image sequence, thus we accumulate moving regions through the image sequence. The boundaries of moving regions are found by Canny edge detector and the foreground region is separated in each frame of the sequence. Remaining regions are defined as background regions. Extracted backgrounds in each frame are combined and reframed as an integrated single background. Based on the estimated background, we compute the frame difference (FD) of each frame. Regions with the FD larger than the threshold are defined as foreground regions, boundaries of foreground regions are defined as unknown regions and the rest of regions are defined as backgrounds. Segmentation information that classifies an image into foreground, background, and unknown regions is called a trimap. Matting process can extract an alpha matte in the unknown region using pixel information in foreground and background regions, and estimate the values of foreground and background pixels in unknown regions. The proposed video matting approach is adaptive and convenient to extract a foreground automatically and to composite a foreground with a background that is different from the original background.

Keywords: Background estimation, Object segmentation, Blockmatching algorithm, Video matting.

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Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

Abstract:

Autoregressive Moving average (ARMA) is a parametric based method of signal representation. It is suitable for problems in which the signal can be modeled by explicit known source functions with a few adjustable parameters. Various methods have been suggested for the coefficients determination among which are Prony, Pade, Autocorrelation, Covariance and most recently, the use of Artificial Neural Network technique. In this paper, the method of using Artificial Neural network (ANN) technique is compared with some known and widely acceptable techniques. The comparisons is entirely based on the value of the coefficients obtained. Result obtained shows that the use of ANN also gives accurate in computing the coefficients of an ARMA system.

Keywords: Autoregressive moving average, coefficients, back propagation, model parameters, neural network, weight.

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Authors: A. Arockia Selvakumar, R. Sivaramakrishnan, Srinivasa Karthik.T.V, Valluri Siva Ramakrishna, B.Vinodh.

Abstract:

Industrial robots play a vital role in automation however only little effort are taken for the application of robots in machining work such as Grinding, Cutting, Milling, Drilling, Polishing etc. Robot parallel manipulators have high stiffness, rigidity and accuracy, which cannot be provided by conventional serial robot manipulators. The aim of this paper is to perform the modeling and the workspace analysis of a 3 DOF Parallel Manipulator (3 DOF PM). The 3 DOF PM was modeled and simulated using 'ADAMS'. The concept involved is based on the transformation of motion from a screw joint to a spherical joint through a connecting link. This paper work has been planned to model the Parallel Manipulator (PM) using screw joints for very accurate positioning. A workspace analysis has been done for the determination of work volume of the 3 DOF PM. The position of the spherical joints connected to the moving platform and the circumferential points of the moving platform were considered for finding the workspace. After the simulation, the position of the joints of the moving platform was noted with respect to simulation time and these points were given as input to the 'MATLAB' for getting the work envelope. Then 'AUTOCAD' is used for determining the work volume. The obtained values were compared with analytical approach by using Pappus-Guldinus Theorem. The analysis had been dealt by considering the parameters, link length and radius of the moving platform. From the results it is found that the radius of moving platform is directly proportional to the work volume for a constant link length and the link length is also directly proportional to the work volume, at a constant radius of the moving platform.

Keywords: Three Degrees of freedom Parallel Manipulator (3DOF PM), ADAMS, Work volume, MATLAB, AUTOCAD, Pappus- Guldinus Theorem.

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Authors: Zhiguo Ren, Lilong Cai

Abstract:

This paper present an effective method to accurately reconstruct and measure the 3D curve edges of small industrial parts based on stereo vision. To effectively fit the curve of the measured parts using a series of line segments in the images, a strategy from coarse to fine is employed based on multi-scale curve fitting. After reconstructing the 3D curve of a hole through a curved surface, its axis is adjusted so that it is parallel to the Z axis with least squares error and the dimensions of the hole can be calculated on the XY plane easily. Experimental results show that the presented method can accurately measure the dimensions of round holes through a curved surface.

Keywords: Stereo Vision, 3D Round Hole Measurement, Curve Fitting, 3D Curve Reconstruction, Least Squares Error.

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Authors: Ellips Masehian, Yalda Katebi

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This paper presents a new sensor-based online method for generating collision-free near-optimal paths for mobile robots pursuing a moving target amidst dynamic and static obstacles. At each iteration, first the set of all collision-free directions are calculated using velocity vectors of the robot relative to each obstacle and target, forming the Directive Circle (DC), which is a novel concept. Then, a direction close to the shortest path to the target is selected from feasible directions in DC. The DC prevents the robot from being trapped in deadlocks or local minima. It is assumed that the target's velocity is known, while the speeds of dynamic obstacles, as well as the locations of static obstacles, are to be calculated online. Extensive simulations and experimental results demonstrated the efficiency of the proposed method and its success in coping with complex environments and obstacles.

Keywords: Dynamic Environment, Moving Target, RobotMotion Planning.

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Authors: Wei-Jong Yang, Yu-Siang Su, Pau-Choo Chung, Jar-Ferr Yang

Abstract:

Moving object detection (MOD) is an important issue in advanced driver assistance systems (ADAS). There are two important moving objects, pedestrians and scooters in ADAS. In real-world systems, there exist two important challenges for MOD, including the computational complexity and the detection accuracy. The histogram of oriented gradient (HOG) features can easily detect the edge of object without invariance to changes in illumination and shadowing. However, to reduce the execution time for real-time systems, the image size should be down sampled which would lead the outlier influence to increase. For this reason, we propose the histogram of uniformly-oriented gradient (HUG) features to get better accurate description of the contour of human body. In the testing phase, the support vector machine (SVM) with linear kernel function is involved. Experimental results show the correctness and effectiveness of the proposed method. With SVM classifiers, the real testing results show the proposed HUG features achieve better than classification performance than the HOG ones.

Keywords: Moving object detection, histogram of oriented gradient histogram of oriented gradient, histogram of uniformly-oriented gradient, linear support vector machine.

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Authors: P. Latha, L. Ganesan, N. Ramaraj, P. V. Hari Venkatesh

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Motion detection is a basic operation in the selection of significant segments of the video signals. For an effective Human Computer Intelligent Interaction, the computer needs to recognize the motion and track the moving object. Here an efficient neural network system is proposed for motion detection from the static background. This method mainly consists of four parts like Frame Separation, Rough Motion Detection, Network Formation and Training, Object Tracking. This paper can be used to verify real time detections in such a way that it can be used in defense applications, bio-medical applications and robotics. This can also be used for obtaining detection information related to the size, location and direction of motion of moving objects for assessment purposes. The time taken for video tracking by this Neural Network is only few seconds.

Keywords: Frame separation, Correlation Network, Neural network training, Radial Basis Function, object tracking, Motion Detection.

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Authors: Ibraheem K. Ibraheem

Abstract:

The aim of this research is to design and implement line-tracking mobile robot. The robot must follow a line drawn on the floor with different color, avoids hitting moving object like another moving robot or walking people and achieves color sensing. The control system reacts by controlling each of the motors to keep the tracking sensor over the middle of the line. Proximity sensors used to avoid hitting moving objects that may pass in front of the robot. The programs have been written using micro c instructions, then converted into PIC16F887 ATmega48/88/168 microcontrollers counterparts. Practical simulations show that the walking robot accurately achieves line following action and exactly recognizes the colors and avoids any obstacle in front of it.

Keywords: Color sensing, H-bridge, line following, mobile robot, PIC microcontroller, obstacle avoidance, phototransistor.

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Authors: Hang-cheong Wong, Pak-kin Wong, Chi-man Vong, Zhengchao Xie, Shaojia Huang

Abstract:

Automotive engine air-ratio plays an important role of emissions and fuel consumption reduction while maintains satisfactory engine power among all of the engine control variables. In order to effectively control the air-ratio, this paper presents a model predictive fuzzy control algorithm based on online least-squares support vector machines prediction model and fuzzy logic optimizer. The proposed control algorithm was also implemented on a real car for testing and the results are highly satisfactory. Experimental results show that the proposed control algorithm can regulate the engine air-ratio to the stoichiometric value, 1.0, under external disturbance with less than 5% tolerance.

Keywords: Air-ratio, Fuzzy logic, online least-squares support vector machine, model predictive control.

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Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.

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Authors: Y. Areepong

Abstract:

The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL₀). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL₁) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL₀) and (ARL₁) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL₁).

Keywords: Average Run Length1, Optimal parameters, Exponentially Weighted Moving Average (EWMA) control chart.

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Authors: Arian Bahrami, Amir Teimourian

Abstract:

In this paper, the effect of the moving platform size on the workspace volume of 6–6 cable-suspended parallel robots is investigated in details for different geometric configurations and orientations of the moving platform. The obtained hints can be used as a rule of thumb in designing this type of robot.

Keywords: Cable-suspended parallel robot, system analysis and design, workspace analysis.

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Authors: A. T. Boum, L. Bitjoka, N. N. Léandre, S. Bennet

Abstract:

This paper presents the estimation of the key parameters of a double fed induction machine (DFIM) by the use of the moving horizon estimator (MHE) for control and monitoring purpose. A study was conducted on the behavior of this observer in the presence of some faults which can occur during the operation of the machine. In the first case a stator phase has been suppressed. In the second case the rotor resistance has been multiplied by a factor. The results show a good estimation of different parameters such as rotor flux, rotor speed, stator current with a very small estimation error. The robustness of the observer was also tested in the practical case of DFIM by using another model different from the real one at a constant close. The very small estimation error makes the MHE a good software sensor candidate for monitoring purpose for the DFIM. 

Keywords: Doubly fed induction machine, moving horizon estimator parameters’ estimation.

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Authors: Wararit Panichkitkosolkul

Abstract:

The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.

Keywords: Autoregressive, Ordinary least squares, Type I error, Power of the test, Monte Carlo simulation.

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Authors: K. Petcharat, Y. Areepong, S. Sukparungsri, G. Mititelu

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These paper, we approximate the average run length (ARL) for CUSUM chart when observation are an exponential first order moving average sequence (EMA1). We used Gauss-Legendre numerical scheme for integral equations (IE) method for approximate ARL0 and ARL1, where ARL in control and out of control, respectively. We compared the results from IE method and exact solution such that the two methods perform good agreement.

Keywords: Cumulative Sum Chart, Moving Average Observation, Average Run Length, Numerical Approximations.

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