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Applying the Mahalanobis–Taguchi System to. Improve Tablet PC Production Processes. Chi-Feng Peng 2,†, Li-Hsing Ho 3,†, Sang-Bing Tsai. The purpose of this paper is to present and analyze the current literature related to developing and improving the Mahalanobis-Taguchi system (MTS) and to. ABSTRACT. The Mahalanobis-Taguchi System is a diagnosis and predictive method for analyzing patterns in multivariate cases. The goal of this study is to.

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Accordingly, the optimization model becomes. Due to its cost and simplicity, resistance spot welding is the dominant joining process in the autoindustry. The ROC is beneficial because it provides a tool to show the advantages represented by true positives versus disadvantages represented by false positives of the classifier relating to data density.

Each weld has 28 features, which represents the dynamic resistance value in the 28 half cycles or welding time. Cost-sensitive methods use both data and algorithmic approaches, where the objective is to optimize i. Even with such unrealistic assumption, Naive Bayes still found noticeable success stories comparable with other types of sophisticated classifiers, for example, NB used in text classification [ 47 ], medical diagnosis [ 48 ], and systems performance management [ 49 ]. In the case of highly imbalanced data, one-class learning showed good classification results [ 28 ].

The case presented will be in the manufacturing sector in the area of resistance spot welding.

Modified Mahalanobis Taguchi System for Imbalance Data Classification

The constant current control tqguchi a current stepper, one Ampere per weld, to compensate for the increase in the electrode diameter or what is known as mushrooming effect. Unfortunately, MTS lacks a method for determining an efficient threshold for the binary classification. Using the negative observations only, reference Mahalanobis Distances are calculated using 1 with all features used.

Knowing the cost matrices in most systfm is practically difficult. View at Google Scholar I.

On the other hand, specificity can be understood as systsm accuracy of the negative observations: Table 2 contains a description of the selected datasets properties. Therefore, the problem of finding the optimum threshold can be reformulated into the problem of finding the closest point that lies on the curve to point. The criterion for selecting the appropriate features is determined by selecting the features that possess high MD values for the positive observations.

The proposed model, Algorithm 1provides an easy, reliable, and systematic way to determine the threshold for the Mahalanobis Taguchi System MTS and its variants i.


For example, the given dataset consists of ninety percent of negative observations and ten percent of positive ones.

It includes the following types: This assessment can be translated into the problem of classifying the dynamic resistance profile input signal for those welds into normal or abnormal welds. While data and algorithmic approaches constitute the majority efforts in the area of imbalanced data, several other approaches have also been conducted, which will be reviewed in Literature Review.

The following optimization model is used to determine the optimum threshold that discriminates between the negative and the positive observations, depending on minimizing the Cartesian distance between the MMTS ROC classifier curve and the theoretical optimum point i. If the classifier ignores the positives observations and classifies all instances as negative, it means that the classifier has ninety percent accuracy i. In this case, the training data was 1, observations i.

Calculation of the Mahalanobis Distance MD using the negative observation is performed first, followed by scaling i.

If the stopping criteria are met, then the training stage is done, and the model is ready for testing observations.

The MTS approach starts with collecting considerable observations from the investigated dataset, tailed by separating of the unhealthy dataset i. The idea of the SVMs classifier is based on establishing the most appropriate hyperplane that separates class observations from each other Figure 2.

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Changing the threshold will change the point location on the curve i. The author declares that there are no conflicts of interest regarding the publication of this paper. If the data distribution of one class is different from distributions of others, then the data is considered imbalance. The Mahalanobis Distances MD for the positive observations are also calculated by using the same equation with all features, with the inverse of the correlation matrix of the negative observation used.

View at Scopus B. The assumption of an equal number of observations in each class is elementary in using the common classification methods such as decision tree analysis, Support Vector Machines, discriminant analysis, and neural networks [ 6 ]. Unfortunately, the PTM method is based on previously assumed parameters, and the accuracy of the classification results was less than the benchmarked classifiers this is one of the findings in this research, which will be discussed in Results.

As mentioned before, will be used as the main metric, but the results for other metrics will be reported here for future researchers to use.


Cost-sensitive methods used different costs or penalties for different misclassification types. Both the MGA and MTS Particle Swarm Optimization methods deal with the Taguchi system orthogonal array part, while the threshold determination still lacks a solid foundation or is hard to be determined in reality. The first work regarding SVMs was published by Cortes and Vapnik [ 42 ], continued by significant contributions from other researchers [ 43 ].

The problems reported in data approaches are as follows: In this paper, a nonlinear optimization model with the objective of minimizing the Euclidean distance between MTS classifier ROC curve and the theoretical optimal point i.

Selection of the new features is performed by using the orthogonal array approach; then a recalculation of MDs for the systej and the positive observation is performed. View at Scopus Taaguchi. In order to assess the suggested algorithm, the MMTS has been benchmarked with several popular algorithms: A set of data is sampled from both classes.

Recently worldwide competition pushes automotive OEMs to improve their productivity, reduce nonvalue added activity, and reduce cost. A rough method for determining the threshold is to plot the positive and negative MD observations versus their orders and decide upon the threshold manually.

In this section, an overview of the benchmarked classifiers, with their parameters, and the machine specifications used for analysis will be presented. Unfortunately one of the bit falls for using this approach is that it can be computationally expensive [ 30 ].

It can be seen clearly that the MMTS outperforms the other classifiers. Table 8 shows the values obtained from comparing the performances of the classifiers between any two classifiers using the Mann—Whitney test and the resulting classifiers rank.

Now, the true positive rate and the false negative rate at the threshold can be defined as. The next step is to determine the threshold that will be used to discriminate the negative observations from the positive ones based on the MD magnitude, which means that the new tagguchi can be classified into either a positive or negative observation according to the following criteria: On the other hand, one-class learning [ 2425 ] used the target class only to determine if the new observation belongs to this class or not.