CN101551886A - Application of KPI analysis based on principal component method in telecom industry income guarantee system - Google Patents

Abstract

In present telecom industry, the information technology is greatly applied, corporation management information basically implements informatization, thus, the informatization data not strong on decision supporting capacity, analysis capability to data in the corporation can not achieve require. Especially, on application of income guarantee, the evaluate on data quality is difficult to be quantized. The invention discloses a KPI analysis method based on a principal component method, which is applied in the telecom industry income guarantee system, can obtain specific reference index by model building through utilizing corporation internal data, constructing KPI and applying the KPI analysis method based on the principal component method, and is a method for showing corporation situation such as corporation data quality and flow path efficiency, and then makes corporation focusing the infection of variable to income.

Description

The application of KPI analysis in the telecommunications industry income guarantee system based on principal component analysis

Technical field:

The present invention relates to telecommunications industry income guarantee field.Be specifically a kind of utilize inside data of enterprise by modeling, make up KPI, and draw concrete reference index by KPI analytical approach based on principal component analysis, the method for situations such as business data quality, flow path efficiency is described.

Background technology:

Current era is the epoch of infotech, particularly in telecommunications industry, infotech has obtained a large amount of application, enterprise operation information has realized informationization basically, yet these informationalized data are not strong to the decision support ability of operator, and enterprises can't reach requirement to the analysis ability of data.Particularly in the application of income guarantee, the evaluation of data quality etc. is difficult to quantize.The present invention provides a cover solution for this problem.

In telecommunications industry income guarantee field, the application process of KPI is still blank basically at present.

Annotate: TMF (international telecommunication management forum) to the definition of income guarantee is: under the situation that does not influence demand, increase profit, income and cash flow by improving the quality of data and improving operation flow.

Annotate: Key Performance Indicator method (Key Performance Indicators, KPI) be a kind of important performance examination instrument, it is monitored controlling movable effect by to setting up the input end relevant with various control activities, the key parameter of output terminal to be provided with, to take a sample, to calculate, to analyze.Can weigh the efficient of each link in data performance and the system well, play the effect of better controlled and evaluation.

The analytical model of principal component analysis

With n system's link being investigated be considered as n sample wherein each sample p index arranged.

1, with original sample matrix X=(x _Ij) _{N * p}In sample value x _IjStandardization $y_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}-\stackrel{\‾}{x_j}}{\sqrt{\mathrm{Var}\left(x_j\right)}}$ (i=1,2 ..., n; J=1,2 ... p), thus obtain standardization decision matrix Y=(y _Ij) _{N * p}(x in the formula _IjJ evaluation of estimate of i index for each system; y _IjBe the later desired value of standardization; x _jWith

Be respectively the sample average and the standard deviation of j evaluation of estimate).

2, compute matrix Y=(y _Ij) _{N * p}Index correlation matrix R, ask the eigenvalue of relevant correlation matrix R ₁〉=λ ₂〉=L 〉=λ _p〉=0, and orthonormalization proper vector ω _j=[ω _J1, ω _{J2, L}, ω _Jp] ^T, j=1,2 ..., p

3, if $\underset{n=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_n=p,$ Claim Be the contribution rate of sample major component, contribution rate is sent out in the accumulation of computation of characteristic values poor $E=\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_k{\left[\underset{n=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\λ}}_n\right]}^{-1},$ With E 〉=85% o'clock, the smallest positive integral of m is as the value of m, and promptly the number of major component is the m of E 〉=85% o'clock.

4, extract preceding m major component $y_k=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{u}_{\mathrm{kj}}{x}_j,(k=\mathrm{1,2},L,m)$

5, be the weight coefficient summation with the variance contribution ratio, calculate the comprehensive evaluation index value of each measured object $F=\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{\mathrm{\α}}_k{y}_k,$ In the formula: α _kIt is the variance contribution ratio of k major component; y _kBe k major component.Size according to the F value is estimated system.

Summary of the invention:

In order to find a kind of evaluation of enterprises business that can in the telecommunications industry income guarantee system, use and the method for data health status, solve the difficulty that enterprise can't quantize the evaluation of data situation, flow path efficiency etc., make the influence of these variablees of enterprises pay attention to income, the present invention begins one's study and finishes.

Principal component analysis can be used for saying something the aid decision making analysis with the influential numerous indexs of analysis are reduced to a few index.

The application of KPI analysis in the telecommunications industry income guarantee system based on principal component analysis

Above-mentioned analytical model is done creationary application in the telecommunications industry income guarantee system as follows:

That 1, lists a certain evaluation and test value in the telecommunications industry income guarantee system influences major component p;

2, choose n mutual incoherent sample, each sample is got the value of its each dimension, obtain original sample matrix X=(x _Ij) _{N * p}

3, each sample dimension values is done standardization and obtain standardization decision matrix Y=(y _Ij) _{N * p}

4, calculate the correlation matrix R and the orthonormalization proper vector ω of decision matrix _j=[ω _J1, ω _{J2, L}, ω _Jp] ^T

5, calculate the contribution rate of sample major component and calculate m;

6, extracting preceding m major component is the weight coefficient summation with the variance contribution ratio, calculates comprehensive evaluation index value F.

7, by the F value evaluation and test value is estimated itself.

By application process as can be seen, by this method, in the end p dimension can be reduced to m, just can express by this m dimension and will get the desired value F that p dimension values carried out comprehensive evaluation originally.Reached to simplify and calculated, the convenient purpose that realizes system applies.

Description of drawings:

Fig. 1: income guarantee assessment indicator system figure

Embodiment:

Income guarantee KPI is from broadly being divided into the quality of data (Data Quality), income leakage (Revenue Leakage) and treatment efficiency (ProcessEfficiency) and income guarantee management (Revenue Assurance Management) four big classification.We are the performance evaluation performance index system of income guarantee, and abstract is as shown in Figure 1 structure (p=9,9 dimensions).

For avoiding commercial affairs to divulge a secret, the raw data of certain telecommunications enterprise has been carried out suitable processing, obtain the PSTN value-added service of this telecommunications enterprise day, commercial affairs are navigated, the call bill data of Best Tone Service (number of samples n=3).

Table 1: the call bill data of certain telecommunications enterprise day

In the last table, line data is represented corresponding 9 indexs, and column data is represented 3 corresponding index observed readings of system.Wherein, owing to index 3 and index 4 are that rising along with the quality of data descends, so these two indexs are carried out change process (1-x _5j) afterwards,, raw data is carried out standardization according to the method for principal component analysis (PCA), obtain the standardization matrix and be

Table 2: the data after the standardization

The covariance matrix of trying to achieve raw data is

$s=\left[\begin{array}{ccccccccc}2.44& 0.815& 2042.1& 1145.3& 0.227& 842.5& 3359.2& -0.273& 3.1\\ 0.815& 0.3396& 674.6917& 352.4& 0.0737& 277.665& 1115.43& -0.0812& 0.9967\\ 2042.1& 674.6917& 2327858.8149& 1017115& 194.105& 712385& 2824223& -247.853& 2669.833\\ 1145.3& 352.4& 1017114.5& 776161& 123.34& 425082.5& 1628969& -207.035& 1762\\ 0.227& 0.0737& 194.105& 123.34& 0.0223& 80.465& 316.19& -0.031& 0.31\\ 842.5& 277.665& 712385& 425082.5& 80.465& 294583& 1166371& -104.06& 1108.5\\ 3359.2& 1115.43& 2824223& 1628969& 316.19& 1166371& 4636108& -393.11& 4335\\ -0.273& -0.0812& -247.8533& -207.035& -0.031& -104.06& -393.11& 0.0566& -0.4483\\ 3.1& 0.9967& 2669.8333& 1762& 0.31& 1108.5& 4335& -0.4483& 4.3333\end{array}\right]$

And try to achieve the correlation matrix of index

Calculate eigenwert and the corresponding quadrature standardized feature vector thereof of R, and be 1, listed eigenwert and the contribution rate and the accumulative total variance contribution ratio of part major component in the table 3 according to the major component number that the condition of E 〉=85% has determined to be used for modeling.

Table 3: the eigenwert of part major component, contribution rate and contribution rate of accumulative total

The relational expression that can be tried to achieve preceding 1 major component by the proper vector that obtains is

y ₁=0.3371x ₁+ 0.3265x ₂+ 0.3462x ₃+ 0.3211x ₄+ 0.3450x ₅+ 0.3434x ₆+ 0.3406x ₇-0.2971x ₈+ 0.3436x ₉From above-mentioned expression formula as can be seen, the contribution rate of first principal component is 0.933, illustrate that first principal component is very big to the influence of net result. after the linear weighted function to each major component, again m major component is weighted summation, promptly getting final evaluation of estimate, because this example has only a major component, so as long as it is weighted. flexible strategy are the variance contribution ratio of each major component:

F＝8.3967y ₁

＝2.8305x ₁+2.7415x ₂+2.8767x ₃+2.6961x ₄+2.8969x ₅+2.8834x ₆+2.8599x ₇-2.4947x ₈+2.8851x ₉

Data after the substitution standardization conversion just can obtain comprehensive evaluation value and ordering, and it is as shown in the table.

Professional	F	Rank
			The PSTN value-added service	47.94	1
Best Tone Service	-10.2977	2
			Commercial affairs are navigated	-17.4909	3

Table 4: the ticket quality situation rank that each is professional

By above operation result as can be known, each business is according to the ordering of the ticket situation of evaluation index, with practical business ticket situation be corresponding to.The result of this routine gained conforms to the actual result of appraisal, though major component KPI analytic approach has certain subjectivity when obtaining sample, as long as sample data is fair and reasonable relatively, net result is not had too big influence.

Claims (2)

1, a kind of KPI analytical approach based on principal component analysis, the particularly application in the telecommunications industry income guarantee system, this method may further comprise the steps:

A, list a certain evaluation and test value in the telecommunications industry income guarantee system influence major component p;

B, choose n mutual incoherent sample, each sample is got the value of its each dimension, obtain original sample matrix X=(x _Ij) _{N * p}

C, each sample dimension values is done standardization obtain standardization decision matrix Y=(y _Ij) _{N * p}

The correlation matrix R and the orthonormalization proper vector ω of D, calculating decision matrix _j=[ω _J1, ω _{J2, L}, ω _Jp] ^T

The contribution rate of E, calculating sample major component is also calculated m;

M major component is the weight coefficient summation with the variance contribution ratio before F, the extraction, calculates comprehensive evaluation index value F.

G, come the evaluation and test value is estimated itself by the F value.

2, as claim a kind of described a kind of KPI analytical approach based on principal component analysis, it is characterized in that by this method, in the end p dimension can be reduced to m, just can express by this m dimension and will get the desired value F that p dimension values carried out comprehensive evaluation originally.Reached to simplify and calculated, the convenient purpose that realizes system applies.