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

On-line recognition of abnormal patterns in bivariate autocorrelated process using random forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time. Meanwhile, the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics. This goes against the statistical I.I.D assumption in using the multivariate control charts, which may lead to the performance of multivariate control charts collapse soon. Meanwhile, the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation, and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities. This study proposed a pattern recognition model using Random Forest (RF) as pattern model to detect and identify the abnormalities in bivariate autocorrelated process. The simulation experiment results demonstrate that the model is superior on recognition accuracy (RA) (97.96%) to back propagation neural networks (BPNN) (95.69%), probability neural networks (PNN) (94.31%), and support vector machine (SVM) (97.16%). When experimenting with simulated dynamic process data flow, the model also achieved better average running length (ARL) and standard deviation of ARL (SRL) than those of the four comparative approaches in most cases of mean shift magnitude. Therefore, we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process. Although bivariate autocorrelated process is focused in this study, the proposed model can be extended to multivariate autocorrelated process control

Recognition of Process Disturbances for an SPC/EPC Stochastic System Using Support Vector Machine and Artificial Neural Network Approaches

Because of the excellent performance on monitoring and controlling an autocorrelated process, the integration of statistical process control (SPC) and engineering process control (EPC) has drawn considerable attention in recent years. Both theoretical and empirical findings have suggested that the integration of SPC and EPC can be an effective way to improve the quality of a process, especially when the underlying process is autocorrelated. However, because EPC compensates for the effects of underlying disturbances, the disturbance patterns are embedded and hard to be recognized. Effective recognition of disturbance patterns is a very important issue for process improvement since disturbance patterns would be associated with certain assignable causes which affect the process. In practical situations, after compensating by EPC, the underlying disturbance patterns could be of any mixture types which are totally different from the original patterns. This study proposes the integration of support vector machine (SVM) and artificial neural network (ANN) approaches to recognize the disturbance patterns of the underlying disturbances. Experimental results revealed that the proposed schemes are able to effectively recognize various disturbance patterns of an SPC/EPC system

Life jacket

Anyone who cannot swim well should wear life jacket whether they are in the water or around the water. Even those who are can swim well should wear the life jacket when they are doing activity such as swimming, fishing, boating or while doing any water-related activity. Life jacket is a kind of safety jacket that keeping the wearer float the in the water. The wearer may be in the conscious or unconscious condition but by wearing the life jacket we can minimize the risk of drowning because life jacket assist the wearer to keep floating in the water

A modelling-oriented scheme for control chart pattern recognition

Control charts are graphical tools that monitor and assess the performance of production processes, revealing abnormal (deterministic) disturbances when there is a fault. Simple patterns belonging to one of six types can be observed when a fault is occurring, and a Normal pattern when the process is performing under its intended conditions. Machine Learning algorithms have been implemented in this research to enable automatic identification of simple patterns. Two pattern generation schemes (PGS) for synthesising patterns are proposed in this work. These PGSs ensure generality, randomness, and comparability, as well as allowing the further categorisation of the studied patterns. One of these PGSs was developed for processes that fulfil the NIID (Normally, identically and independently distributed) condition, and the other for three first-order lagged time series models. This last PGS was used as base to generate patterns of feedback-controlled processes. Using the three aforementioned processes, control chart pattern recognition (CCPR) systems for these process types were proposed and studied. Furthermore, taking the recognition accuracy as a performance measure, the arrangement of input factors that achieved the highest accuracies for each of the CCPR systems was determined. Furthermore, a CCPR system for feedback-controlled processes was developed

Recognition of Concurrent Control Chart Patterns in Autocorrelated Processes Using Support Vector Machine

Control chart pattern recognition (CCPR) is an important issue in statistical process control because unnatural control chart patterns (CCPs) exhibited on control charts can be associated with specific causes that adversely affect the manufacturing processes. In recent years, many machine learning techniques have been successfully applied to CCPR. However, such existing research for CCPR has mostly been developed for identification of basic CCPs (Shift Patterns, Trend Patterns, Cyclic Pattern and Systematic Pattern). Little attention has been given to the identification of concurrent CCPs (two or more basic CCPs occurring simultaneously) which are commonly encountered in practical manufacturing processes. In addition, these existing researches also assume the process data are independently and identically distributed which may not be appropriate for certain manufacturing processes. This study proposes a support vector machine (SVM) approach to identify concurrent CCPsfor a multivariate process with autocorrelated observations which can be characterized by afirst order autoregressive (AR(1)) model. The numerical results indicate that the proposed model can effectively identify two concurrent identical CCPs but for those cases involving one trend pattern and one shift pattern, their recognition accuracy deteriorates to around 20% to 50% depending on the autocorrelation coefficients used in the data model

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Control chart patterns recognition with constrained data

Recognition and classification of non-random patterns of manufacturing process data can provide clues to the possible causes that contributed to the product defects. Early detection of abnormal process patterns, particularly in highly precise and rapid automated manufacturing is necessary to avoid wastage and catastrophic failures. Towards this end, various control chart patterns recognition (CCPR) methods have been proposed by researchers. Most of the existing control chart patterns recognizers assumed that data is fully available and complete. However, in reality, process data streams may be constrained due to missing, imbalanced or inadequate data acquisition and measurement problems, erroneous entries and technical failure during data acquisition process. The aim of this study is to investigate and develop an effective recognition scheme capable of handling constrained control chart patterns. Various scenarios of data constraints involving missing rates, missing mechanisms, dataset size and imbalance rate were investigated. The proposed scheme comprises the following key components: (i) characterization of input data stream, (ii) imputation and feature extraction, and (iii) alternative recognition schemes. The proposed scheme was developed and tested to recognize the constrained patterns, namely, random, increasing/decreasing trend, upward/downward shift and cyclic patterns. The effect of design parameters on the recognition performance was examined. The Exponentially-Weighted Moving Average (EWMA) imputation, oversampling and Fuzzy Information Decomposition (FID) were investigated. This research revealed that some constraints in the dataset can eventually change the distribution and violate the normality assumption. The performance of alternative designs was compared by mean square error, percentage of correct recognition, confusion matrix, average run length (ARL), t-test, sensitivity, specificity and G-mean. The results demonstrated that the scheme with an ANNfuzzy recognizer trained using FID-treated constrained patterns significantly reduce false alarms and has better discriminative ability. The proposed scheme was verified and validated through comparative studies with published works. This research can be further extended by investigating an adaptive fuzzy router to assign incoming input data stream to an appropriate scheme that matches complexity in the constrained data streams, amongst others

Identification of abnormal patterns in AR (1) process using CS-SVM

Using machine learning method to recognize abnormal patterns covers the shortage of traditional control charts for autocorrelation processes, which violate the applicable conditions of the control chart, i.e., the independent identically distributed (IID) assumption. In this study, we propose a recognition model based on support vector machine (SVM) for the AR (1) type of autocorrelation process. For achieving a higher recognition performance, the cuckoo search algorithm (CS) is used to optimize the two hyper-parameters of SVM, namely the penalty parameter c and the radial basis kernel parameter g. By using Monte Carlo simulation methods, the data sets containing samples of eight patters are generated in experiments for verifying the performance of the proposed model. The results of comparison experiments show that the average recognition rate of the proposed model reaches 96.25% as the autocorrelation coefficient is set equal to 0.5. That is apparently higher than those of the SVM model optimized by the particle swarm optimization (PSO) or the genetic algorithm (GA). Another experiment result demonstrates that the average recognition accuracy of the CS-SVM model also reaches higher than 95% for different autocorrelation levels. At last, a lot of data streams in or out of control are simulated to measure the ARL values. The results turn out that the model has an acceptable online performance. Therefore, we believe that the model can be used as a more effective approach for identification of abnormal patterns in autocorrelation process

Control Charts to Enhance Quality

Control charts are important tools of statistical quality control to enhance quality. Quality improvement methods have been applied in the last few 10 years to fulfill the needs of consumers. The product has to retain the desired properties with the least possible defects, while maximizing profit. There are natural variations in production, but there are also assignable causes which do not form part of chance. Control charts are used to monitor production; in particular, their application may serve as an “early warning” index regarding potential “out-of-control” processes. In order to keep production under control, different control charts which are prepared for dissimilar cases are established incorporating upper and lower control limits. There are a number of control charts in use and are grouped mainly as control charts for variables and control charts for attributes. Points plotted on the charts may reveal certain patterns, which in turn allows the user to obtain specific information. Patterns showing deviations from normal behavior are raw material, machine setting or measuring method, human, and environmental factors, inadvertently affecting the quality of product. The information obtained from control charts assists the user to take corrective actions, hence opting for specified nominal values enhancing as such quality