Journal of Industrial Engineering, University of Tehran, Special Issue, 2011, PP. 1-12 1
Applying Mahalanobis –Tagouchi System in Detection of
High Risk Customers –A case-based study in an Insurance Company

Seyedeh Elaheh Abbasi 1, Abdollah Aaghaie *1 and Mahboubeh Fazlali 2

Department. of Industrial Engineering, K.N.Toosi University of Technology, Tehran, Iran
Research and Development Department of MAPNA Group, Tehran, Iran
(Received 10 October 2010, Accepted 4 June 2011)

The organizations use all appropriate tools to improve their service to the customers. The detection of especial customers and the forecast of their behavior undoubtedly can play an important role in improvement of service. In this paper, a new statistical method called the Mahalanobis Taguchi system has been used for this purpose. This method is used for the analysis of real data of an insurance company and five big cities in Iran are considered. There are seven initial factors which is important in the occurrence of accidents and losses. These factors are reduced to four. Customer’s behavior is analyzed case by case by the Mahalanobis– distance concept. In fact with using this new method, demand of customers case by case was analyzed and it is an important outcome in analyzing behavior of customers. Devising ways to prevent the accidents and damages will need the recognition of Customer’s behavior. The neural networks method is used to recognize the high–risk customers, and the results of this method are compared with the results of Mahalanobis–Taguchi system. The results show that Mahalanobis– Taguchi system with its abnormality scale has a great capability in recognizing high-risk customer. To recognize the customer by the Mahalanobis Taguchi system is more accurate in comparison with the neural networks method.

Keywords: Mahalanobis – Taguchi system, Mahalanobis distance, Vehicle insurance, High – risk customers, Neural networks

* Corresponding author: Tel: +98- 21- 84063363 Fax: +98- 21- 88674858 Email: [email protected]

Daily increasing population and consequently increasing travels inside and between the cities has caused more car accidents and heavy financial loss and casualties and injuries which have made an inevitable care on behalf of insurance companies .Insurance companies are important organizations which can play an important role in people’s convenience by providing appropriate services to them. Today, Vehicle and collision insurance organizations have outstood among all the other service presenting organizations. Detection of effective factors in occasion of an accident and inflicted damages to the vehicle and also the analyze manner of customers for detection customers that inflict a high loss to a company, undoubtedly can play an important role in planning and improvement of service and decisions. For that to take place, we have used a relative new statistical method titled: Mahalanobis – Taguchi System (MTS). This method which is in fact a mixture of Taguchi test model & the Mahalanobis Distance (MD) concept has been offered by Genichi Taguchi in 1996 in order to determine templates in different fields to classify data [1], [2]. This method is a multivariate analyses method which is for some reasons better those other methods which are common in this field [3]. Some researches and usages to already use this method are: Cudney and Colleagues to concisely present MTS method and have a review on different papers on the field [4]. In another paper, they used this method to reduce factors which are effective on the customer’s satisfaction in the fields of transportation to reduce 6 factors to 5 factors [5].
Vivek V.Khanzode and J.Maiti used MTS method to detect more important factor among 11 total factorswhich has been effective in iron casting quality [6]. HsiaoLin Teng and Yu-Cheng Lee used MTS method to predict financial crisis in electronic industry of Taiwan [7] and reduced the 42 effective primary detected variants to 7 factors. K.Ganesanand Mahalakshmi used MTS method to detect effective and principal factors in choosing suitable domains for fishing [8]. Chih-Ming Liu and colleagues used amixed algorithm of MTS and neural network method to process data in a dynamic space [9]. Maiti.J and Avishek Pal offered a method to improve efficiency of MTS method [10].
Shubhabarata Datta and Prasun Das used MTS in the fields of the effects of chemical compounds on metal products [11]. A.G.Olabi and EM.Anawa and also Ibrahim Sonat used this method in plastic welding and injection and brought about a satisfactory end [12], [13]. Yang T and Cheng Y-T used MTS method to improve flip-chip bumping height inspection efficiency[14].Taguchi used MTS method aimed at improving weaknesses of previous methods used in this fields [15]. Actually the Mahalanobis distance is used to establish a measurement scale and Taguchi method to optimize the target system [16]. In this paper we try to apply potentials of MTS methods to improve insurance organizations services to the customers of Vehicle Collision
The Mahalanobis – Taguchi System has been used in various fields and has proved as a system showing acceptable results. In this paper the purpose is to show the potential ability of this method to improve insurance systems. Customers who cause high loss form a remarkable part of total loss and recognizing these customers is important for insurance companies. So in this paper, these customers were considered and are called high-risk customers. With results of this research, insurance companies can analyze behavior of their customers case by case, regarding their demand of company. The most important methods that are used in analyzing customer’s demand are: cause and effect (regression) methods, time series and neural networks. But considering the time series models abilities, they cannot recognize a specific group of customers and then analyze their demands, because they deal with demand of whole customers. In fact, previous demands are analyzed and future demands are estimated. These customers are a minority and have higher demands, so they behave like outlier data, so multivariate regression methods are not suitable due to sensitivity to outlier data. But neural networks have binary scale and this property can be useful for this purpose. Therefore neural networks were applied for comparison with output results of MTS. To accomplish this, we used real data of customers who had their cars insured in a certain insurance company during 2007 and 2008. Using these data, important factors in a collision accident and the resulted damage was detected; and based on those; to assess validity; we detected some customers who had inflicted a high loss to the insurance company in 2008. The results show that MTS with its abnormality scale has a great capability in recognizing these customers and is more accurate in comparison with the neural networks method. In fact with using MTS, the demand of customers can be analyzed case by case and it is an important outcome in analyzing behavior of customers.

1. MTS method
1.1. Mahalanobis distance
Mahalanobis distance is a distance which was offered by P.C.Mahalanobis in1936; and is established on the base of the relation between variants of which different templates can be detected and analyzed. This is a useful method to determine the similarity between an unknown sample series and a known sample series. This distance is different from Euclidian distance by 2 means: first by maintaining the correlation between data, second by independency from measurement scale.
Mahalanobis distance for a multivariate vector x from a group of values with the average µ and Covariance Matrix S is defined as Eq.(1).

MD =

If each dimension of a multi-dimension is normally distributed and after sampling these dimensions stand independent from each other, samples shape like a spherical. In such a case if we want to determine a given position of a point in this space in relation with the spherical pace, it can be judged by concepts such Average and Standard Deviation in the spherical space and comparison with the given point. But what actually takes place is that, normally in multi-dimensional spaces, all spaces are connected one another and not independent. In such a situation, normal distributions are or in linear relation or there is no relation between them; so there is a linear relation between them and in fact there is a correlation between them. In such a situation, the resulted space is elliptical due to the correlation; so in such a case in the relative angle of the point in relation with space is important in addition to average and standard deviation. In other words, the density of points in an elliptical space has also to be considered.
Here was applied covariance matrix between the elliptical space points and bring up Mahalanobis distance concept. In figure 1, Mahalanobis distance which is a direct distance similar to Euclidian distance but differentiates the densities between points in space, is shown .the Mahalanobis distance is calculated in relation with the centre of points which create the elliptical space. This elliptical space is called base or normal Mahalanobis space.

1.2. Taguchi design of experiments
In 1940, Dr.Taguchi brought up new statistical concepts and latters on these concepts proved useful and precious in fields of quality control and development .since the time, many Japanese industrialists take up the method to improve process and product quality. The enhancing quality of vehicles made in this country is strongly involved with widely use of the method. To design of experiment, Taguchi applies some standard tables named orthogonal table or matrix .e.g. If there is 7 factors each in 2 levels, i.e. 128 tests, he use standard table L8. We use these orthogonal tables in required calculations in this paper. 8 designed tests are shown instead of 128 tests. Taguchi says in case that all factors have 2 levels, factors could be accidentally positioned in columns .since, in MTS method only 2 level is justified, here, only a simple 2 level form is considered. To continue the design of experiment, after design of details according the orthogonal tables, the result of each test is to be determined and after that according to the result we should make decisions. This step brings up the concept of Signal to Noise Ratio.









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