KR101291502B1 - System and method for analyzing online game loyalty of user - Google Patents

Abstract

The online game customer loyalty analysis system 100 according to the present invention includes a questionnaire result database 410 for storing a questionnaire result, a psychological index extractor 420 for extracting a questionnaire item related to a psychological index from the stored questionnaire results, Experience index extractor 430 for extracting a questionnaire item related to the empirical index from the stored survey results, loyalty index extractor 440 for extracting a questionnaire item related to the loyalty index from the stored survey results, stored survey results The structural equation model application unit 450 applies the extracted items from the psychological index extraction unit 420 and the experiential index extraction unit 430 to the structural equation model composed of the observation variable according to and the latent variable according to the path coefficient between the observation variables. A weight calculator configured to calculate a weight to be reflected in an item extracted by the loyalty index extractor 440 from the structural equation model ( 460 and the loyalty index calculator 470 that calculates the online game loyalty index by calculating the weight calculated by the weight calculator 460 to the items extracted by the loyalty index extractor 440.

Description

Online game customer loyalty analysis system and analysis method {SYSTEM AND METHOD FOR ANALYZING ONLINE GAME LOYALTY OF USER}

The present invention relates to a customer loyalty analysis system and analysis method. In particular, the present invention relates to an online game customer loyalty analysis system and analysis method.

Customer Satisfaction Management refers to a marketing-oriented management method in which a company's success depends on its customers, and conducts corporate activities aimed at maximizing customer satisfaction. The customer satisfaction is explained by the disagreement theory that the customer's satisfaction is formed by the difference between the customer's expectation and performance, or by comparing the customer's performance with the company's cost and the company's profit. This is explained by the theory of fairness that satisfaction occurs when you feel more gained. It is also explained by the value-perception discrepancy theory that consumers set their own value criteria for performance and are satisfied when performance exceeds this. However, it is difficult to measure all three of the above theories.

In order to quantify such customer satisfaction, there are methods such as the Customer Satisfaction Index (CSI) as an external measurement index, and as the internal measurement index, the Employee Satisfaction Index (ESI), the Customer Orientation Index (COI), and the Interval Customer Satisfaction Index (ICSI). And the like.

Among these methods, CSI analysis method is one of active methods of listening to customers' opinions along with Focus Group Index (FGI), Service Survey (SS), Initial Quality Survey (IQS), etc. One of the means of evaluating overall corporate activities used to identify performance of satisfaction activities, to compare priorities with companies, to determine priorities for future business activities, and to control the revision and complementation of strategies for customer activities. Form. Therefore, the CSI can be used more widely when competition is intensifying as a means of evaluating activities of the entire enterprise.

To date, the following methods have been suggested for such CSI analysis. The evaluation item of satisfaction is described as an example.

1) Single item evaluation method

In case of CS (Customer Satisfaction) survey, the correlation coefficient between overall satisfaction and dimension (sector, attribute) or detail item satisfaction is very high (0.7 ~ 0.8 level), because most items or service satisfaction depend on each other. . Based on this evidence, the CSI can be calculated using only the overall satisfaction question.

2) How to evaluate multiple items

As a method of calculating the arithmetic mean of satisfaction of each service item, this method is mainly used in a product or service industry in which the importance of each item is not highly discriminated. CS surveys with a large number of dimensions and a large number of samples tend not to show significant differences in their importance.

3) Multi-item weighted average method

As a method of multiplying and multiplying the satisfaction in consideration of the importance of each dimension (sector, attribute) or subitem, the weight is considered according to the degree of influence on the overall satisfaction of the customer. However, the satisfaction level of each sub-item can be viewed as a result of decomposition of the overall satisfaction, and the sum of these results in calculating the overall satisfaction has a disadvantage in that more errors can occur than directly measuring the overall satisfaction.

4) How to reflect loyalty

Although the result of satisfaction is directly reflected in the 'purchasing intention' and 'other recommendation intention' directly to the CSI, there is a disadvantage in that a clear theoretical basis for the weight is insufficient.

5) structural equation model

It is a method of calculating CSI by estimating the correlation structure among satisfaction points of each service point by a model.

The methods for calculating importance in the above-described CSI analysis methods include Multiple Regression Analysis, Factor Regression Analysis, Simple Correlation Coefficient Analysis, Correlation Coefficient * Calculation of Weight of Regression Coefficient There are statistical methods, such as analysis, and customer-directed methods such as self-rated, anchored measures analysis, and constant-sum measures analysis.

On the other hand, the CSI analysis methods described above are commonly used customer satisfaction measurement methods, and are not effective to apply to customer loyalty measurement of online games including various external and internal factors and various characteristics of customer recognition. There was this.

Accordingly, an object of the present invention is to divide the loyalty-related factors for online games into psychological index area, experience index area, and loyalty index area, and perform statistical estimation on each area and the detailed items of each area through structural equation model. By providing an effective online game loyalty analysis system and analysis method.

In addition, the object of the present invention is to classify the factors related to online game loyalty into sub-items such as re-use intention, recommendation intention, positive word-of-mouth intention, reassurance confidence or intention to ignore other game benefits, and the weight for the sub-items is a structural equation model By estimating by providing an effective online game loyalty analysis system and analysis method.

The solution to the problem of the present invention is not limited to those mentioned above, and other solutions not mentioned can be clearly understood by those skilled in the art from the following description.

The online game customer loyalty analysis system according to the present invention includes a survey result database in which a survey result is stored, a psychological index extractor extracting a survey item related to a psychological index from the stored survey result, and an experience index from the stored survey result. The experience index extractor extracts the related survey item results, the loyalty extractor extracts the survey item results related to the loyalty index from the stored survey results, the observation variables according to the stored survey results, and the potential variables according to the path coefficients between the observation variables. A structural equation model application unit for applying the extracted items from the psychological index extraction unit and the experiential index extraction unit to the constructed structural equation model, a weight calculation unit calculating a weight to be reflected in the items extracted from the loyalty index extraction unit from the structural equation model; Items extracted from the Loyalty Index Extractor Calculating the weights calculated by the weight calculation section and comprises parts of loyalty index calculator for calculating an online game loyalty index.

The questionnaire item related to the psychological index according to the present invention is characterized by including any one or more of loneliness factor or perceived stress factor.

Loneliness factors according to the present invention include any one or more of the absence of friends, the absence of people to rely on, the feeling of abandonment, the sense of alienation, the absence of necessary friends, the degree of misery or the absence of true friends.

Perceived stressors according to the present invention include any one or more of poor work process, confidence in work process, smooth work process or limit of ability.

The questionnaire item related to the experiential index according to the present invention includes any one or more of character homogeneity factor, immersion factor or pleasure factor.

Character homogeneity factor according to the present invention includes any one or more of the sense of self-confident, character unity, goal matching or the same presence in the game.

Immersion factors in accordance with the present invention include any one or more of time forgetting, game concentration, fast time lapse or game immersion.

Pleasant factors according to the present invention include any one or more of fun, interest, pleasure or attraction.

The questionnaire item related to the loyalty index according to the present invention includes one or more of reuse intention, recommendation intention, positive word of mouth intention, reassurance of reuse, or disregard of other game benefits.

The method may further include a correlation information database in which a path coefficient according to the present invention is stored.

The loyalty index according to the present invention is characterized by being calculated by the following equation.

OG_LI = X ₁ × W ₁ + X ₂ × W ₂ + X ₃ × W ₃ + X ₄ × W ₄ + X ₅ × W ₅

Here, X ₁ is reuse intention, X ₂ is recommendation intention, X ₃ is positive word of mouth intention, X ₄ is reuse intention, X ₅ is intent to ignore other game benefits, W ₁ , W ₂ , W ₃ , W ₄ And W ₅ is X ₁ , Are the weights for X ₂ , X ₃ , X _4, and X ₅ , and W ₁ , W ₂ , W ₃ , W ₄ And The sum of W ₅ is one.

In the online game customer loyalty analysis method of the online game customer loyalty analysis system using the survey according to the present invention, when the result of the survey is stored in the database of the online game customer loyalty analysis system, the online game customer loyalty index is calculated. The loyalty analysis system observes the survey result data extracted in the step S1 and the step S1 of the survey results stored in the database, the survey result data related to the psychological index, the related survey result data and the experience index, according to the survey result. Step S2 is applied to the structural equation model consisting of latent variables according to the path coefficient between the variable and the observed variable, and the survey results related to loyalty are extracted from the survey results stored in the database. Computing the loyalty index of the online game customer through the step S3 of calculating the weight for each item and the S4 step of reflecting the weight of each item calculated in the step S3 in the questionnaire results related to the loyalty.

The loyalty index according to the present invention is characterized by being calculated by the following equation.

OG_LI = X ₁ × W ₁ + X ₂ × W ₂ + X ₃ × W ₃ + X ₄ × W ₄ + X ₅ × W ₅

Here, X ₁ is reuse intention, X ₂ is recommendation intention, X ₃ is positive word of mouth intention, X ₄ is reuse intention, X ₅ is intent to ignore other game benefits, W ₁ , W ₂ , W ₃ , W ₄ And W ₅ is X ₁ , Are the weights for X ₂ , X ₃ , X _4, and X ₅ , and W ₁ , W ₂ , W ₃ , W ₄ And The sum of W ₅ is one.

According to the present invention, the loyalty-related factors for online games are divided into psychological index area, experiential index area, and loyalty index area, and each area and the detailed items of each area are effectively performed by performing statistical estimation through a structural equation model. There is an advantage in analyzing online game loyalty.

According to the present invention, the factors related to online game loyalty are divided into detailed items such as reuse intention, recommendation intention, positive word of mouth intention, reassurance of reuse or intention to ignore other game benefits, and the weights of the detailed items are determined by a structural equation model. By estimating, there is an advantage to effectively analyze online game loyalty.

The effects of the present invention are not limited to those mentioned above, and other effects not mentioned can be clearly understood by those skilled in the art from the following description.

1 is a diagram illustrating the concept of an online game customer loyalty analysis model according to the present invention.
2 is a diagram illustrating a questionnaire on the questionnaire for analyzing online game customer loyalty according to the present invention.
3 is a diagram illustrating a structural equation model for analyzing online game customer loyalty according to the present invention.
4 is a block diagram schematically showing the configuration of an online game customer loyalty analysis system according to the present invention.
5 is a flowchart schematically illustrating a sequence of an online game customer loyalty analysis method according to the present invention.

As used herein, the singular " include "should be understood to include a plurality of representations unless the context clearly dictates otherwise, and the terms" comprises & , Parts or combinations thereof, and does not preclude the presence or addition of one or more other features, integers, steps, components, components, or combinations thereof.

Hereinafter, an online game customer loyalty analysis system and analysis method will be described in detail with reference to the accompanying drawings.

1 is a diagram illustrating a concept of an online game customer loyalty analysis model 100 according to the present invention. Referring to FIG. 1, each of the sub-items related to online game loyalty is divided into a psychological index area 110, an experiential index area 120, and a loyalty index area 130. As a correlation, we will create a structural equation model. Based on the structural equation model generated based on this, statistical estimation of online game loyalty is performed. In FIG. 1, each region is grouped by a dotted line.

The psychological index area 110 includes the loneliness factor 111, the perceived stress factor, and the like. The loneliness factor 111 may include the absence of friends (1), the absence of people to rely on (2), the feeling of abandonment (3), the feeling of alienation (4), the need of friends (5), the degree of misery (6) and the true absence of friends (7). ), And the perceived stress factor 112 is a factor related to poor work process (1), confidence in work process (2), smooth work process (3), and limit of ability (4).

Table 1 below shows an example of the questionnaire for the loneliness factor 111, and Table 2 shows an example of the questionnaire for the perceived stressor 112. The order of items is the same as the order of the detailed items for each of the factors described above.

The exponential index area 120 includes a character homogeneity factor 121, a pleasure factor 122, an immersion factor 123, and the like. The character homogeneity factor 121 is related to the sense of self-confidence (the character feels as the user's alter ego, (1), the sense of unity (2), the sense of unity (3) and the same presence (4) with the character in the game, and the enjoyment factor ( 122 is related to fun (1), interest (2), enjoyment (3) and attraction (4), etc., and the immersion factor 123 is time oblivion (1), game concentration (2), fast time lapse ( 3) and game immersion (4) and the like.

Table 3 below shows an example of the questionnaire for the character homogeneity factor 121, Table 4 shows an example of the questionnaire for the perceived pleasure factor 122, and Table 5 shows an example of the questionnaire for the immersion factor 123. Indicates. The order of items is the same as the order of the detailed items for each of the factors described above.

Meanwhile, the above-mentioned questionnaire item is composed of a seven-point scale. According to the example of the questionnaire, various forms such as a 5-point scale or a 10-point scale may be used. Since the scale may involve subjectivity of the respondent due to subjectivity, it is preferable to clearly name each section. It is preferable to divide and convert 100 points equally in the section of each scale. Equation 1 below is a formula for converting equally divided 100 points according to the scale.

Here, X is a score evaluated by the respondent, N is the number of scales, and Y is a score converted into 100 points. FIG. 2 shows a questionnaire scale for analyzing online game loyalty when there are 7 scales as in the above-described questionnaire.

The loyalty index area 130 reflects weights on detailed items such as reuse intention (1), recommendation intention (2), positive word of mouth intention (3), confidence in reuse (4), and intention to ignore other game benefits (5). Is calculated. Table 6 below shows an example of a questionnaire about the game loyalty factor 131.

Each weight should be appropriately weighted according to the type of game, survey subject, survey purpose, and the like.

Each of the aforementioned index regions, factors belonging to each index region, and sub-items belonging to each factor are correlated by predetermined path coefficients. Furthermore, appropriate statistical techniques should be used in surveys to take into account the correlation between overall loyalty and loyalty to specific items.

In the present invention, the loneliness factor 111 and the perceived stress factor 112, which are psychological factors, have a correlation that affects the empirical factor homogeneity factor 121 and the immersion factor 123.

3 is a diagram illustrating a structural equation model for analyzing online game customer loyalty according to the present invention. Referring to FIG. 3, as described with reference to FIG. 1, the results of each questionnaire are classified by factors, and the relationship between each factor is constituted by a structural equation model to statistically estimate online game customer loyalty.

In FIG. 1, rectangular items that classify each question item mean Observed Variables in the structural equation. Observation variables are variables that are directly measured, and are connected to latent variables to measure latent variables. In this case, the latent variable refers to a variable in which a construct is not directly observed or measured, and is indirectly measured by the observed variable. Items shown as circles or ellipses in FIGS. 1 and 3 mean latent variables in the structural equations.

Meanwhile, in the structural equation, the arrow connection between the observation variable and the latent variable or the arrow connection between the latent variables means a path coefficient between each variable.

Therefore, each observation variable shown in FIG. 1 is measured as a survey result value of a questionnaire classified into the corresponding variable, and reflects a predetermined path coefficient to each of the measured observation variable values of the corresponding latent variable connected with each observation variable and an arrow. The value is calculated.

For example, the potential variable value of the loneliness factor is calculated by reflecting the path coefficient to the observation variable value by the questionnaire result value for the sub-items belonging to the loneliness factor 111 such as a friend absence, a person to rely on, or a feeling of abandoned. The latent variable value of the perceived stress factor 112 is calculated by reflecting the path coefficient to the observed variable value based on the questionnaire result value for the lack of processing, work processing confidence, smooth work processing, and ability limitation. The remaining factors are also used to calculate latent variable values.

On the other hand, the latent variable of the game loyalty factor 131 in the structural equation reflects the path coefficient of the game loyalty factor 131 in the immersion factor 123 to the value of the latent variable of the immersion factor 123 in the experience exponential region 120. Is calculated.

As such, the structural equation model enables statistical estimation of online game loyalty. Meanwhile, in the structural equation model of the present invention, the path coefficient value considered between the variables is determined by various methods such as user setting.

4 is a block diagram schematically showing the configuration of an online game customer loyalty analysis system 400 according to the present invention.

The online game customer loyalty analysis system 400 according to the present invention includes a questionnaire result database 410 in which a questionnaire result is stored, a psychological index extractor 420 extracting a questionnaire item related to a psychological index from the stored questionnaire results, Experience index extractor 430 for extracting a questionnaire item related to the empirical index from the stored survey results, loyalty index extractor 440 for extracting a questionnaire item related to the loyalty index from the stored survey results, psychological index extractor 420 and the weight equation calculator 460 that calculates the weight to be reflected in the loyalty index calculator 470 from the structural equation model, and the structural equation model application unit 450 applying the items extracted by the exponent index extractor 430. ), Calculate the online game loyalty index by calculating the weight calculated by the weight calculator 460 to the item extracted by the loyalty index extractor 440. Includes calculating loyalty index 470.

The questionnaire item related to the psychological index includes one or more of the loneliness factor 111 or the perceived stress factor 112.

The loneliness factor 111 includes one or more of the absence of friends, no one to rely on, abandoned feelings, feelings of alienation, absence of friends when necessary, a degree of misery, or absence of true friends.

Perceived stress factors 112 include one or more of poor work process, confidence in process, smooth work process, or limit of ability.

The questionnaire item related to the experience index includes one or more of the character homogeneity factor 121, the immersion factor, or the pleasure factor 122.

The character homogeneity factor 121 includes any one or more of a sense of self, a sense of unity, a goal match, or the same presence in the game.

Immersion factors include any one or more of time forgetting, game concentration, fast time lapse, or game immersion.

Pleasure factor 122 includes one or more of fun, excitement, enjoyment, or attractiveness.

The questionnaire items related to the loyalty index include one or more of reuse intention, recommendation intention, positive word of mouth intention, reassurance of reuse, or ignoring other game benefits.

Meanwhile, the system of the present invention may further include a correlation information database in which a path coefficient is stored.

The online game loyalty index according to the present invention may be calculated by Equation 2 below.

Here, X ₁ is reuse intention, X ₂ is recommendation intention, X ₃ is positive word of mouth intention, X ₄ is reuse intention, X ₅ is intent to ignore other game benefits, W ₁ , W ₂ , W ₃ , W ₄ And W ₅ is X ₁ , Are the weights for X ₂ , X ₃ , X _4, and X ₅ , and W ₁ , W ₂ , W ₃ , W ₄ And The sum of W ₅ is one.

Although the explanation of weights focuses on loyalty only, it is clear that the details of all factors, that is, the items surveyed, may reflect different weights.

5 is a flowchart schematically illustrating a sequence of an online game customer loyalty analysis method according to the present invention.

In the online game customer loyalty analysis method according to the present invention, when the survey result is stored in the database of the online game customer loyalty analysis system 400, the loyalty index of the online game customer is calculated.

Specifically, the online game customer loyalty analysis system 100 is a survey extracted in the step S1, the step S1 is extracted from the survey results data related to the psychological index and the relevant survey result data and experience index among the survey results stored in the database The result data is extracted from the S2 step applied to the structural equation model consisting of the observation variable according to the survey result and the latent variable according to the path coefficient between the observation variables, and the survey result related to loyalty is extracted from the survey results stored in the database. Through step S3 of calculating item weights of the survey results related to loyalty and S4 step of reflecting the item weights calculated in step S3 to the survey results related to loyalty, through these steps to calculate the loyalty index of online game customers Will be calculated.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. It will be understood that variations and specific embodiments which may occur to those skilled in the art are included within the scope of the present invention.

100: online game customer loyalty analysis model 110: psychological index area
111: Loneliness factor 112: Perceived stress factor
120: experience index area 121: character homogeneity factor
122: pleasure zone 123: immersion factor
130: loyalty index area 131: game loyalty factor
400: Online Game Customer Loyalty Analysis System
410: survey results database 420: psychological index extraction unit
430: experience index extraction unit 440: loyalty index extraction unit
450: structural equation model application unit 460: weight calculation unit
470: loyalty index calculator

Claims (13)

In the customer loyalty analysis system using an itemized survey,
A questionnaire result database that stores a questionnaire item result related to a psychological index, a questionnaire item result related to an experience index, and a questionnaire item result related to a loyalty index;
A psychological index extraction unit for reading a questionnaire item result related to the psychological index from the questionnaire result database;
An experience index extraction unit for reading a questionnaire item result related to the experience index from the questionnaire result database;
A loyalty index extraction unit for reading a questionnaire item result related to the loyalty index from the questionnaire result database;
Applying a structural equation model applying a questionnaire result related to the psychological index and a questionnaire item related to the empirical index to the observation variable based on a structural equation model consisting of an observation variable and a latent variable according to a path coefficient between the observation variables. part;
A weight calculator configured to calculate a weight to be reflected in a questionnaire item related to the loyalty index from the structural equation model; And
A loyalty index calculator configured to calculate an online game loyalty index by calculating a weight calculated by the weight calculator to a questionnaire item result related to the loyalty index,
The questionnaire item results are stored in the questionnaire results database in the form of a score X evaluated by the respondent during the N point scale for each question item presented as an N point scale from 1 point to N point,
The structural equation model application unit uses the following equation from the form of a score X in which a respondent evaluates the survey item results on the N point scale.

Online game customer loyalty analysis system, characterized in that the conversion in the form of a 100 point conversion score Y according to the structural equation model. The method of claim 1,
The survey item related to the psychological index is
An on-line gaming customer loyalty analysis system comprising any one or more of loneliness factors or perceived stressors. The method of claim 2,
The loneliness factor is
An online game customer loyalty analysis system comprising any one or more of: absence of friends, no one to rely on, feeling abandoned, alienation, absence of necessary friends, misery, or absence of true friends. The method of claim 2,
Perceived stressors
An on-line game customer loyalty analysis system comprising any one or more of poor job processing, job processing confidence, smooth processing, or a sense of limitation in ability. The method of claim 1,
The survey items related to the experience index
An online game customer loyalty analysis system comprising any one or more of character homogeneity factor, immersion factor or pleasure factor. The method of claim 5,
The character homogeneity factor is
An on-line game customer loyalty analysis system comprising any one or more of a sense of self, a sense of character, a sense of goal, or a presence in a game. The method of claim 5,
The immersion factor is
An online game customer loyalty analysis system comprising one or more of time forgetting, game concentration, fast time lapse, or game immersion. The method of claim 5,
Pleasure factor
An online gaming customer loyalty analysis system comprising at least one of fun, excitement, enjoyment or attraction. The method of claim 1,
The questionnaire item related to the loyalty index is
An online gaming customer loyalty analysis system comprising any one or more of: reuse intention, recommendation intention, positive word of mouth intention, reuse confidence, or disregard of other game benefits. The method of claim 1,


The online game customer loyalty analysis system, characterized in that it further comprises a correlation information database that stores the path coefficient. The method of claim 1,
The loyalty index is an online game customer loyalty analysis system, characterized in that calculated by the following equation.
OG_LI = X ₁ × W ₁ + X ₂ × W ₂ + X ₃ × W ₃ + X ₄ × W ₄ + X ₅ × W ₅
(Where X ₁ is reuse intent, X ₂ is referral intent, X ₃ is positive word of mouth intent, X ₄ is reuse intent, X ₅ is intent to ignore other games, W ₁ , W ₂ , W ₃ , W ₄ And W ₅ is each X ₁ , X ₂ , X ₃ , X ₄ And a weight for X ₅ , wherein W ₁ , W ₂ , W ₃ , W ₄ And Sum of W ₅ is 1) In the online game customer loyalty analysis method using a survey,
Read questionnaire results related to the psychological index and questionnaire results related to the experience index from a questionnaire results database that store questionnaire results related to the psychological index, questionnaire results related to the experience index, and questionnaire results related to the loyalty index. The step;
Applying a questionnaire item result related to the psychological index and a questionnaire item result related to the experience index to the observation variable based on a structural equation model composed of an observation variable and a latent variable according to a path coefficient between the observation variables;
Calculating weights to be reflected in a questionnaire item related to the loyalty index through the structural equation model; And
Reading a questionnaire item result related to the loyalty index from the questionnaire result database, and calculating an online game loyalty index by applying the weight to the questionnaire item result related to the loyalty index,
The questionnaire item results are stored in the questionnaire results database in the form of a score X evaluated by the respondent during the N point scale for each question item presented as an N point scale from 1 point to N point,
The survey item results are expressed in the following equation from the form of the score X evaluated by the respondent during the N point scale.

Online game customer loyalty analysis method, characterized in that converted into the form of a 100 point conversion score Y according to the structural equation model. The method of claim 12,
The loyalty index is an online game customer loyalty analysis method, characterized in that calculated by the following equation.
OG_LI = X ₁ × W ₁ + X ₂ × W ₂ + X ₃ × W ₃ + X ₄ × W ₄ + X ₅ × W ₅
(Where X ₁ is reuse intent, X ₂ is referral intent, X ₃ is positive word of mouth intent, X ₄ is reuse intent, X ₅ is intent to ignore other games, W ₁ , W ₂ , W ₃ , W ₄ And W ₅ is each X ₁ , Is a weight for X ₂ , X ₃ , X ₄ and X ₅ , wherein W ₁ , W ₂ , W ₃ , W ₄ And Sum of W ₅ is 1)

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