Method of lines and runge-kutta method in solving partial differential equation for heat equation

Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method

Cumulative sum quality control charts design and applications

Includes bibliographical references (pages 165-169).Classical Statistical Process Control Charts are essential in Statistical Control exercises and thus constantly obtained attention for quality improvements. However, the establishment of control charts requires large-sample data (say, no less than I 000 data points). On the other hand, we notice that the small-sample based Grey System Theory Approach is well-established and applied in many areas: social, economic, industrial, military and scientific research fields. In this research, the short time trend curve in terms of GM( I, I) model will be merged into Shewhart and CU SUM two-sided version control charts and establish Grey Predictive Shewhart Control chart and Grey Predictive CUSUM control chart. On the other hand the GM(2, I) model is briefly checked its of how accurate it could be as compared to GM( I, 1) model in control charts. Industrial process data collected from TBF Packaging Machine Company in Taiwan was analyzed in terms of these new developments as an illustrative example for grey quality control charts

The Effect of Measurement Error on X̃-R̃ Fuzzy Control Charts

Control charts are tools used for monitoring manufacturing processes. Fuzzy Set Theory has found its way in control charts and new types of fuzzy control charts, with different capabilities, has been introduced. In this paper, a process in which the result of the measuring of each piece is imprecise is studied, and a X̃-R̃ fuzzy control chart is used for monitoring. The aim is to study the effect of measurement error on the effectiveness of the fuzzy control chart to detect out of control situations. The model used in this research is a linear covariate model. ARL parameters are used to study the performance of the fuzzy control chart when the parameters of covariate model is increased or decreased

A Fuzzy Control Chart Approach for Attributes and Variables

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach ha

Inclined ergometer to enhance FES-assisted indoor rowing exercise performance

Improving the FES-assisted indoor rowing exercise (FES-rowing) performance enables the spinal cord injury (SCI) people to perform hybrid FES-exercise in a higher level of intensity. High level of exercise volume and intensity can play a big role in prevention of cardiovascular disease, type 2 diabetes and obesity which is a significant threat to the health of people with chronic SCI. FES-rowing can be enhanced to achieved the high level exercise through the arrangement of the rowing ergometer. In this paper, the performance of FES-rowing using an adjustable inclined rowing ergometer is investigated. Two different methods to enhance the FES-rowing performance using inclined ergometer are implemented. A model of the adjustable inclined ergometer and humanoid are developed using the Visual Nastran (vN4D) software environment and validated by the experimental work. Fuzzy logic control is implemented to control the knee and elbow trajectories for smooth rowing manoeuvre. The generated level of electrical stimulations for activation of quadriceps and hamstrings muscles are recorded and analysed. The FES-rowing efficiency for both methods have been defined and illustrated. The results show the inclined ergometer with upper body effort is the best performance in enhancing the FES-rowing

A Variable Control Chart Based on Process Capability Index Under Generalized Multiple Dependent State Sampling

This paper proposed a process capability index-based control chart under the new extended form of multiple-dependent state sampling (MDS) named generalized MDS (GMDS). The scheme is based on inner and outer control limits and utilizes the previous state of the samples. The performance comparisons of the proposed chart with the existing charts are made by using out-of-control ARL. The simulation study showed the superiority of the proposed chart over the existing PCI-based control charts under Shewhart and MDS schemes. An empirical illustration is also given to demonstrate the application of the proposed chart.11Ysciescopu

Optimizing the Cost of Integrated Model for Fuzzy Failure Weibull Distribution Using Genetic Algorithm

This research applies the fuzzy concept in development of an integrated model (Statistical process control and Maintenance management) with Weibull distribution for Exponentially Weighted Moving Average (EWMA) control chart. Since sample data may contain uncertainties coming from measurement systems and environment conditions, fuzzy number is used to inspect these suspicions. Moreover, the Weibull distribution with fuzzy scale parameters is considers, and the genetic algorithm approach is used to determine the optimal values of six variables that minimize the fuzzy hourly cost. Finally, the fuzzy hourly cost is transformed to crisp number by the centroid defuzzification.This research applies the fuzzy concept in development of an integrated model (Statistical process control and Maintenance management) with Weibull distribution for Exponentially Weighted Moving Average (EWMA) control chart. Since sample data may contain uncertainties coming from measurement systems and environment conditions, fuzzy number is used to inspect these suspicions. Moreover, the Weibull distribution with fuzzy scale parameters is considers, and the genetic algorithm approach is used to determine the optimal values of six variables that minimize the fuzzy hourly cost. Finally, the fuzzy hourly cost is transformed to crisp number by the centroid defuzzification

Quality of Papers Stems from Authors and Quality of Teaching Stems from Professors

On the web it is very frequently found that good papers are published only in “Peer Reviewed Trusted Journals (PRTJ)”, while low quality papers are published in the “Predatory Publishing Journals”. Here we show that this is not true, because the quality of papers depends on the quality of the authors in the same manner that quality of teaching depends on the quality of professors. Since generally the authors are professors it is important to see the two sides of the “publishing medal”: authors and professors. We will use the SPQR Principle [«Semper Paratus ad Qualitatem et Rationem (Always Ready for Quality and Rationality)»] as the way to analyse papers, books and teaching; it seems that very few people have taken care of Quality of Methods (Deming, Juran, Gell-Mann, Shewhart, Einstein, Galilei). The cases analysed here are from PRT Journals and teaching documents

Statistical fault detection in photovoltaic systems

Faults in photovoltaic (PV) systems, which can result in energy loss, system shutdown or even serious safety breaches, are often difficult to avoid. Fault detection in such systems is imperative to improve their reliability, productivity, safety and efficiency. Here, an innovative model-based fault-detection approach for early detection of shading of PV modules and faults on the direct current (DC) side of PV systems is proposed. This approach combines the flexibility, and simplicity of a one-diode model with the extended capacity of an exponentially weighted moving average (EWMA) control chart to detect incipient changes in a PV system. The one-diode model, which is easily calibrated due to its limited calibration parameters, is used to predict the healthy PV array’s maximum power coordinates of current, voltage and power using measured temperatures and irradiances. Residuals, which capture the difference between the measurements and the predictions of the one-diode model, are generated and used as fault indicators. Then, the EWMA monitoring chart is applied on the uncorrelated residuals obtained from the one-diode model to detect and identify the type of fault. Actual data from the grid-connected PV system installed at the Renewable Energy Development Center, Algeria, are used to assess the performance of the proposed approach. Results show that the proposed approach successfully monitors the DC side of PV systems and detects temporary shading.Peer ReviewedPostprint (author's final draft