CN106021097B - Software reliability growth model method of interval estimation based on test feature - Google Patents

Software reliability growth model method of interval estimation based on test feature Download PDF

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CN106021097B
CN106021097B CN201610304615.2A CN201610304615A CN106021097B CN 106021097 B CN106021097 B CN 106021097B CN 201610304615 A CN201610304615 A CN 201610304615A CN 106021097 B CN106021097 B CN 106021097B
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reliability index
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CN106021097A (en
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刘超
鲍力
杨海燕
吴际
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Beihang University
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    • G06F11/3604—Software analysis for verifying properties of programs
    • G06F11/3608—Software analysis for verifying properties of programs using formal methods, e.g. model checking, abstract interpretation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The software reliability growth model method of interval estimation based on test feature that the present invention relates to a kind of, comprising: test feature is analyzed from multiple angles, corresponding criterion is designed and test feature is measured, obtain test feature measurement results；According to the relationship of test feature measurement results and reliability index, the regression model of reliability index and test feature measurement is constructed；According to the regression model of reliability index and test feature measurement, interval estimation is carried out to reliability index.The present invention measures the method for regression model by building reliability index and test feature to find the relationship between reliability index and test feature, has pure mathematics basis, more scientific and precise；The test feature data generated when using actual test come assist carry out reliability index interval estimation, improve the credibility of Interval Estimator of The Reliability Indexes.

Description

Software reliability growth model method of interval estimation based on test feature
Technical field
The present invention relates to software reliability evaluation technical field more particularly to a kind of software reliabilities based on test feature Index method of interval estimation.
Background technique
Software is ubiquitous in our life, and in various industries every field, software all plays very important Role.In Safety-Critical System, software failure will lead to serious, fatal consequence.The Unpredictability of software defect makes We do not know when software can fail and how to fail.Though the reliability of hardware system is developed in recent years, But the reliability of software systems but cannot still reach our expectation.Exactly because the importance of software reliability and should There are many an open questions, software reliability is receive more and more attention in field.
Software reliability summarizes the reliable of software by probability that software fails as a software metrics index Operation degree.According to the software reliability recommended practice that IEEE is promulgated, software reliability, which refers to, " under the defined conditions and to be provided Time in, software does not cause the ability or probability of thrashing ".Thrashing will cause all multi-risk Systems, such as economic loss, Casualties, so Safety-Critical System requires reliability to reach certain level, it is potentially hazardous in software use to ensure It will not occur.In industrial circle, various software exploitation standard is all strict with Software failure probability, particularly with peace Full critical software.
In software reliability field achievement it is most, it is of greatest concern be software reliability model (Software Reliability Model, SRM) research.Software reliability model collected software failure when being intended to using software test Data, by the method simulation softward failure procedure of modeling, to provide software reliability assurance value.Software reliability model is The software reliability analysis tool most strong with evaluation at present provides foundation to improve software quality.Software Reliability Modeling Main target be to be fitted theoretical distribution of the fail data about the time, be distributed the reliability of assessment software simultaneously according to this And design the rule that can determine software test dwell time.In existing numerous models, NHPP model can by software By Journal of Sex Research, person is widely used.Since average failure number function is directly given by NHPP model, so in some feature time The calculating of average failure number is very simple.Maximum-likelihood estimation can be used in unknown parameter in model or least-squares estimation obtains It arrives.
Software test is characterized in some characterizations about test process and test result, and e.g., reliability is based on survey Test result analyzes the secure status of software, is analyzed usually using multiple reliability indexs.Often due to test process Cover various features, these information during the test how are comprehensively utilized in software reliability evaluation becomes this INVENTION IN GENERAL.
Statistics thinks that interval estimation can portray the precision of point estimation, is a kind of important Statistical Inference.Therefore It needs to construct confidence interval to software reliability model unknown parameter, to more accurately descriptive model estimates of parameters and mould Extent of deviation between shape parameter true value.
At present both at home and abroad to the research method of the interval estimation of reliability model parameter be all directly from reliability model and Fail data itself considers, does not comprehensively consider test feature factor.
Summary of the invention
In view of above-mentioned analysis, the present invention is intended to provide a kind of software reliability growth model interval estimation based on test feature Method, to solve the problems, such as that existing method of interval estimation exists.
The purpose of the present invention is mainly achieved through the following technical solutions:
The software reliability growth model method of interval estimation based on test feature that the present invention provides a kind of, comprising:
Test feature is analyzed from multiple angles, corresponding criterion is designed and test feature is measured, tested Characteristic measure result；
According to the relationship of test feature measurement results and reliability index, reliability index and test feature measurement are constructed Regression model；
According to the regression model of reliability index and test feature measurement, interval estimation is carried out to reliability index.
Further, the test feature measurement results include at least:
The test case that code coverage, demand coverage rate, the code coverage of complexity weighting, complexity density weight Number, test case number of variations, newly-increased failure number.
Further, the reliability index includes at least one or more of following indexs:
Crash rate, reliability, mean time to failure, mean time between failures, crash rate change rate.
Further, crash rate: crash rate pays close attention to failure probability of the software systems within the unit time, is defined asWherein R (t) is reliability function, i.e., the probability to fail does not occur in system operation before t moment, and f (t) is to lose Density function is imitated,
Reliability: the degree of reliability of the attention location system within a period of time, i.e. R (t)；
Mean time to failure: there is the average time of first failure since operation in software, if R (t) is continuous Type function, then
Mean time between failures: concern software systems occur failing twice in operation between Mean Time Between Replacement；
Crash rate change rate: the situation that changes with time that fails in software running process is focused on, is passed through It is calculated, λ (t1) and λ (t2) it is respectively t1And t2The crash rate at moment.
Further, the process for the regression model that building reliability index is measured with test feature specifically includes:
Calculate reliability index；
Determine the citation form of regression model；
Examine influence of the independent variable to reliability index whether significant, retaining influences significant independent variable, the independent variable As test feature measurement results.
Further, the whether significant method of influence for examining independent variable to reliability index includes:
If former regression equation is y=β0+β1x1+…+βi-1xi-1+βixi+βi+1xi+1+…+βpxp, remove variable xiAfter obtain New regression model be y=β0+β1x1+…+βi-1xi-1+βi+1xi+1+…+βpxp, new regression model is referred to as subtracting for former regression model Model, former regression model is referred to as full model, wherein βiIt is the coefficient of regression model independent variable, x indicates that independent variable, y are indicated because becoming Amount, p indicate the number of arguments；
It calculates separately the regression sum of square U of full model and subtracts the regression sum of square U of modeli', to obtain Ui=U-Ui′； After obtaining the corresponding sum of squares of partial regression of each independent variable, the size that more each factor contributes entire regression effect, by tribute Small person is offered to reject；
If the multiple correlation coefficient of full model square be R2, subtract the multiple correlation coefficient of model square isDefinition
Null hypothesisAs null hypothesis H0When being true, test statistics isFor given level of significance α, F is calculated by sample valueiValue, if Fi ≥F1-α(1, n-m-1), then refuse H0, i.e.,It is significantly not zero, this illustrates xiY is had a significant impact, should be added in subtracting model Enter xiMake full model；If Fi< F1-α(1, n-m-1), then receive H0, i.e.,It is significantly zero, this illustrates xiY is influenced not Significantly, x should be rejected in full modeli, make and subtract model；N indicates sample size number, and m indicates the number of arguments.
Further, the process for carrying out interval estimation to reliability index specifically includes:
Assuming that indicating reliability index, x with y1~xpRespectively indicate test feature measurement results, it is assumed that obtained recurrence mould Type is y=β0+β1x1+β2x2+β3x3+...+βpxp+ ε, if it is assumed that different phase reliability index estimated value is mutually indepedent, then Deviation ε Normal Distribution；
In order to be forecast using regression equation, x is being provided1,x2,…,xpA class value x01,x02,…,x0pWhen, remember x0 =(1, x01,x02,…,x0p) ', obtains y0=x '0β+ε0, E (ε0)=0, Var (ε0)=σ2And y0Predicted valueE (X) indicates the mean value of X, and Var (X) indicates the variance of X, σ2Just for standard The variance of state distribution, x '0Indicate x0Transposition；
It can be further derived by by the above propertyThen y0Confidence level be 1- α Confidence interval isT indicates t points Cloth, n-p-1 are the freedom degree of t distribution, and X is multiple groups independent variable (x1,x2,...xp) composition matrix, the transposition of X ' expression X；
In order to simplify mathematical model, it is assumed herein that each stage reliability index estimated value and previous stage reliability index The degree of correlation of estimated value is ρ, if identifying bias vector (ε with Σ1,ε2,...,εn), wherein n indicates test phase number, then Have
If the above different phase reliability index estimated value is assumed to meet independently of each other, ρ=0 in matrix, at this time
It is indicated with WKnow that W is positive definite matrix, there are matrix Z to make Z2=W；
Multiply Z together on the both sides equation Y=XB+ Σ-1Obtain Z-1Y=Z-1XB+Z-1Σ, wherein Y indicates reliability index vector (y1,y2,...,yn) ', X is indicatedB indicates that β vector, Σ indicate that bias vector, p are indicated from change Measure number；After conversion, Var (Z-1Σ)=Z-2Var (Σ)=W-1σ2W=σ2I, if therefore enabling Y*=Z-1Y, X*=Z-1X, Σ*=Z-1Y can be obtained in Σ*=X*B+Σ*, Y*,Σ*Y can be obtained in Normal Distribution*Confidence interval, and then according to Y*=Z-1The confidence interval of Y can be obtained in Y.
The present invention has the beneficial effect that:
The method of regression model is measured by building reliability index and test feature to find reliability index and test Relationship between feature has pure mathematics basis, more scientific and precise.
The test feature data generated when using actual test come assist carry out reliability index interval estimation, improve The credibility of Interval Estimator of The Reliability Indexes.
Other features and advantages of the present invention will illustrate in the following description, also, partial become from specification It obtains it is clear that understand through the implementation of the invention.The objectives and other advantages of the invention can be by written explanation Specifically noted structure is achieved and obtained in book, claims and attached drawing.
Detailed description of the invention
Fig. 1 is the flow diagram of the method for the embodiment of the present invention.
Specific embodiment
Specifically describing the preferred embodiment of the present invention with reference to the accompanying drawing, wherein attached drawing constitutes the application a part, and Together with embodiments of the present invention for illustrating the principle of the present invention.
As shown in FIG. 1, FIG. 1 is the flow diagrams of the method for the embodiment of the present invention, can specifically include following steps:
Step 101: test feature being analyzed from multiple angles, test feature is measured, obtains including such as The measurement results of the following aspects:
Code coverage, demand coverage rate, the code coverage for considering complexity density, the test for considering complexity density Increase failure number between use-case number, test phase between test case number of variations and test phase newly.
Step 102: calculating reliability index, and according to reliability index and test feature measurement results, building is reliable Property index and test feature measurement regression model.That is, proposed adoption Maximum-likelihood estimation or least-squares estimation are reliable to software Property model (such as Schneidewind) unknown parameter carry out point estimation, to be calculated by software reliability model corresponding reliable Property index estimation, then described using the method for recurrence reliability index and test feature measurement between relationship, establish Corresponding regression model.
The reliability index that the present invention is paid close attention to includes: crash rate, reliability, mean time to failure (MTTF), puts down 5 reliability indexs of equal time between failures (MTBF) and crash rate change rate.Crash rate reflects software within the unit time Failure probability, reliability reflection software failure probability whithin a period of time, reliability growth reflection reliability are in a period of time Growth, the variation whithin a period of time of crash rate change rate reflection crash rate, MTTF and MTBF reflection failure time interval Attribute.Each reliability index has specific calculation formula, and core is the parameter of estimation model, once it obtains corresponding Model parameter estimation, so that it may which direct basis formula estimates corresponding software reliability growth model.
5 reliability indexs be specifically defined and calculation method is as follows:
1) crash rate: crash rate pays close attention to failure probability of the software systems within the unit time, is usually indicated with λ.Failure Rate is generally related with time t, and crash rate changes at any time, reflects the variation of reliability.It may be generally defined asWherein R (t) is reliability function, i.e., the probability to fail does not occur in system operation before t moment, and f (t) is to lose Density function is imitated,
2) reliability: the degree of reliability of the attention location system within a period of time, i.e. R (t).If t have exceeded give it is multistage The time range of section test data, then referred to as predicting reliability, otherwise referred to as test phase reliability.This project is not because concern has There are the reliability status analysis for carrying out section plane test, the reliability in Main Analysis test phase.
3) mean time to failure: there is the average time of first failure since operation in software, is abbreviated as MTTF, It may be interpreted as the expected time of software systems no-failure operation.If R (t) is continuous type function,
4) it the mean time between failures: although many times software operation is failed, but still is able to maintain certain Working condition.Mean time between failures concern software systems occur failing twice in operation between Mean Time Between Replacement, It is expressed as MTBF.In practice, crash rate, MTTF and MTBF both can be measured directly by fail data, can also be passed through Selected reliability model is estimated.
5) crash rate change rate: the situation that changes with time that fails in software running process is focused on, mathematically Correspond to the derivative of λ (t).It can pass through in practiceIt is calculated, λ (t1) and λ (t2) it is respectively t1And t2When The crash rate at quarter.
From definition above as can be seen that there is certain derivation relationships between reliability index, if obtaining reliable Degree, then mean time to failure can be acquired directly by integral.Thus obtain the confidence area to one of reliability index Between estimate after, the confidence intervals of other indexs can also be obtained by deriving relationship accordingly.
Reliability index, x are indicated with y1~xpSuch as code coverage, demand coverage rate, complexity is respectively indicated to weight The test features such as code coverage, the test case number of complexity density weighting, test case number of variations, newly-increased failure number because Element.Y and x are described with which kind of curve firstly the need of determiningiThe relationship of (i=1 ..., p).If assuming y and xiBetween be linear Relationship, the then regression model obtained are multiple linear regression model, and citation form is y=β0+β1x1+β2x2+β3x3+...+βpxp+ ε；If describing y and x using exponential curve1Relationship, and y and other x are described using straight lineiThe relationship of (i=2 ..., p), The regression model citation form then obtained isIt can be seen that with not Same curve describes y and xiThe relationship of (i=1 ..., p) will obtain different regression models.In order to solve this problem, I To investigate independent variable xiWith the domain knowledge background of y, if can not still be determined according to domain background using which kind of curve come X is describediIt, then can be according to y about x with yiScatter plot carry out curve type similar in selected shape.
It after determining the citation form of regression model, needs to examine influence of the independent variable to y whether significant, retaining influences to show The independent variable of work, the method for solving this problem can be sum of squares of partial regression or partial F test.
1) sum of squares of partial regression
Regression sum of square U is contribution of all independents variable to the total variance of y.If rejecting a variable, recurrence square With will reduce, the numerical value of reduction it is bigger illustrate the variable contribution it is bigger.We are eliminating independent variable xiRecurrence square afterwards With U reduction numerical value UiReferred to as to variable xiSum of squares of partial regression.
If former regression equation is y=β0+β1x1+…+βi-1xi-1+βixi+βi+1xi+1+…+βpxp, remove variable xiAfter obtain New regression model be y=β0+β1x1+…+βi-1xi-1+βi+1xi+1+…+βpxp, new regression model is referred to as subtracting for former regression model Model, former regression model is referred to as full model.Wherein, βiIt is the coefficient of regression model independent variable, i=1 to 6, x indicates independent variable, y Indicate dependent variable.
It calculates separately the regression sum of square U of full model and subtracts the regression sum of square U of modeli', to obtain Ui=U-Ui′。 After obtaining the corresponding sum of squares of partial regression of each independent variable, can more each factor size that entire regression effect is contributed, So that small person will be contributed to reject.
2) partial F test
If the multiple correlation coefficient of full model square be R2, subtract the multiple correlation coefficient of model square isDefinitionDue to an independent variable x more in full modeli, so ifIt is almost nil to illustrate xiIt is not significant to y It influences.Therefore, here it is null hypothesisWork as H0When being true, test statistics isFor given level of significance α, F is calculated by sample valueiValue, if Fi≥F1-α(1, n-m-1), then refuse H0, i.e.,It is significantly not zero, this illustrates xiY is had a significant impact, should be added in subtracting model Enter xiIt is allowed to referred to as full model.If Fi< F1-α(1, n-m-1), then receive H0, i.e.,It is significantly zero, this illustrates xiY is influenced not Significantly, x should be rejected in full modeli, it is allowed to be known as subtracting model.Wherein, n indicates sample size number, and m indicates the number of arguments.
Step 103: according to the regression model of reliability index and test feature measurement, section being carried out to reliability index and is estimated Meter.After obtaining measuring the regression model with reliability index towards test feature, connection is more on the basis of regression analysis The actual features of stage test estimate confidence interval to reliability index.
By testing a part that the defect for finding and repairing is software all defect, the fail data tested It is an observation sample to all out-of-service sequences of software.Based on the obtained parameter estimation result of the sample not necessarily with software Truth is consistent, therefore the present invention is by the basis of the reliability index of estimation, using test feature measurement results to can Estimating Confidence Interval is carried out by property index, target is to obtain following reliability index result:Its InFor the estimated result of some reliability index (such as MTTF), r be the true reliability index result of software (although unknown, In the presence of), 1- α is confidence level, and w is confidence interval length.The present invention is concerned with how to obtain setting for defined confidence level Believe section.
Software test and Reliability Practice experience have shown that, test feature being capable of concentrated expression test effect, such as test feature In coverage rate factor be able to reflect test for tested software coverage condition, coverage rate is higher, then the later period in testing The invalid cost and trend observed just are more nearly using the failure being likely to occur with software in the future, thus are surveyed based on corresponding The reliability index estimated result that examination data obtain is just closer with achieved reliability index.
This shows test feature to a certain extent and can assist in the length w of the confidence interval of reliability index.This Invention plan constructs the relationship between test feature measurement and reliability index by regression model first, then by returning mould Type provides the confidence interval of reliability index estimated value.
Assuming that indicating reliability index, x with y1~xpCode coverage, demand coverage rate, complexity is respectively indicated to weight The test features such as code coverage, the test case number of complexity density weighting, test case number of variations, newly-increased failure number because Element.Assuming that obtained regression model is y=β0+β1x1+β2x2+β3x3+...+βpxp+ ε, if it is assumed that different phase reliability refers to It is mutually indepedent to mark estimated value, then deviation ε Normal Distribution.
In order to be forecast using regression equation, x is being provided1,x2,…,xpA class value x01,x02,…,x0pWhen, remember x0 =(1, x01,x02,…,x0p) ', obtains y0=x '0β+ε0, E (ε0)=0, Var (ε0)=σ2And y0Predicted valueWherein, E (X) indicates the mean value of X, and Var (X) indicates the variance of X, σ2For mark The variance of quasi normal distribution, x '0Indicate x0Transposition, E () expression takes mean value, and Var () expression takes variance；
With Several Properties once:
(1)It is the Unbiased estimtion of y, i.e.,
(2) in y0All linear unbiased forecasts in,Variance it is minimum；
(3) (0, σ ε~N2In),AndWithIndependently of each other, InFor residual sum of squares (RSS).
It can be further derived by by the above propertyThen y0Confidence level be 1- α Confidence interval is
Wherein, t is indicated T distribution, n-p-1 are the freedom degree of t distribution, and X is multiple groups independent variable (x1,x2,...xp) composition matrix, the transposition of X ' expression X；
However, testing experience according to the practical multistage, rear stage test is usually on the basis of previous stage test The adjustment made, so above with respect to different phase reliability index estimated value mutually independent hypothesis invalid, the latter half Reliability index estimated value to previous stage reliability index estimated value be it is relevant, in order to simplify mathematical model, it is assumed herein that The degree of correlation of each stage reliability index estimated value and previous stage reliability index estimated value is ρ.If identified with Σ Bias vector (ε1,ε2,...,εn), wherein n indicates test phase number, then has
If the above different phase reliability index estimated value is assumed to meet independently of each other, ρ=0 in matrix, at this time
It is indicated with WKnow that W is positive definite matrix, there are matrix Z to make Z2=W.In equation Y The both sides=XB+ Σ are same to multiply Z-1Obtain Z-1Y=Z-1XB+Z-1Σ, wherein Y indicates reliability index vector (y1,y2,...,yn) ', X It indicatesB indicates that β vector, Σ indicate bias vector.After conversion,If therefore enabling Y*=Z-1Y, X*=Z-1X, Σ*=Z-1Y can be obtained in Σ* =X*B+Σ*, Y*,Σ*Y can be obtained in Normal Distribution*Confidence interval, and then according to Y*=Z-1The confidence area of Y can be obtained in Y Between.
In conclusion the embodiment of the invention provides a kind of software reliability growth model interval estimation side based on test feature Method has the following beneficial effects:
(1) method of regression model is measured by building reliability index and test feature to find reliability index and survey The relationship between feature is tried, has pure mathematics basis, more scientific and precise.
(2) ignore test feature compared to traditional existing method and section is directly carried out to reliability index according to fail data Estimation, the test feature data generated when the present invention is using actual test come assist carry out reliability index interval estimation, mention The high credibility of Interval Estimator of The Reliability Indexes.
It will be understood by those skilled in the art that realizing all or part of the process of above-described embodiment method, meter can be passed through Calculation machine program is completed to instruct relevant hardware, and the program can be stored in computer readable storage medium.Wherein, institute Stating computer readable storage medium is disk, CD, read-only memory or random access memory etc..
Although the present invention and its advantage has been described in detail it should be appreciated that without departing from by the attached claims Defined by can carry out various changes, substitution and transformation in the case where the spirit and scope of the present invention.Moreover, the model of the application Enclose the specific embodiment for being not limited only to process, equipment described in specification, means, method and steps.In the art is common Technical staff is from the disclosure it will be readily understood that execution and corresponding reality described herein can be used according to the present invention Apply the essentially identical function of example or process that obtain the result essentially identical with it, that existing and future is to be developed, equipment, Means, method or step.Therefore, the attached claims purport includes such process, equipment, hand in the range of them Section, method or step.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto, In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art, It should be covered by the protection scope of the present invention.

Claims (4)

1. a kind of software reliability growth model method of interval estimation based on test feature characterized by comprising
Test feature is analyzed from multiple angles, corresponding criterion is designed and test feature is measured, obtain test feature Measurement results, the test feature measurement results include such as lower aspect:
The test case number of code coverage, complexity density weighting that code coverage, demand coverage rate, complexity weight, Test case number of variations, newly-increased failure number；
According to the relationship of test feature measurement results and reliability index, the recurrence of reliability index and test feature measurement is constructed Model；
According to the regression model of reliability index and test feature measurement, interval estimation is carried out to reliability index, to reliability The process that index carries out interval estimation specifically includes:
Assuming that indicating reliability index, x with y1~xpRespectively indicate test feature measurement results, it is assumed that obtained regression model is y =β0+β1x1+β2x2+β3x3+β4x4+...+βpxp+ ε, if it is assumed that different phase reliability index estimated value is mutually indepedent, then partially Poor ε Normal Distribution, wherein βiIt is the coefficient of regression model independent variable, 0≤i≤p；
In order to be forecast using regression equation, x is being provided1,x2,… ,xpA class value x01,x02,… ,x0pWhen, remember x0= (1,x01,x02,… ,x0p) ', obtains y0=x '0β+ε0, E (ε0)=0, Var (ε0)=σ2And y0Predicted valueE (X) indicates the mean value of X, and Var (X) indicates the variance of X, σ2Just for standard The variance of state distribution, x '0Indicate x0Transposition, E () expression takes mean value, and Var () expression takes variance；
It can be further derived by by the above propertyThen y0Confidence level be 1- α confidence Section isT indicates t distribution, N-p-1 is the freedom degree of t distribution, and X is multiple groups independent variable (x1,x2,...xp) composition matrix, the transposition of x ' expression X, α is aobvious Work property is horizontal；
In order to simplify mathematical model, it is assumed herein that each stage reliability index estimated value and previous stage reliability index are estimated The degree of correlation of value is ρ, if identifying bias vector (ε with Σ1,ε2,...,εn), wherein n indicates test phase number, then has
If the above different phase reliability index estimated value is assumed to meet independently of each other, ρ=0 in matrix, at this time
It is indicated with WKnow that W is positive definite matrix, there are matrix Z to make Z2=W；
Multiply Z together on the both sides equation Y=XB+ Σ-1Obtain Z-1Y=Z-1XB+Z-1Σ, wherein Y indicates reliability index vector (y1, y2,...,yn) ', X is indicatedB indicates that β vector, Σ indicate bias vector；After conversion, Var(Z-1Σ)=Z-2Var (Σ)=W-1σ2W=σ2I, if therefore enabling Y*=Z-1Y, X*=Z-1X, Σ*=Z-1Y can be obtained in Σ*= X*B+Σ*, Y*,Σ*Y can be obtained in Normal Distribution*Confidence interval, and then according to Y*=Z-1The confidence interval of Y can be obtained in Y.
2. the method according to claim 1, wherein the reliability index includes at least one in following indexs It is a or multiple:
Crash rate, reliability, mean time to failure, mean time between failures, crash rate change rate.
3. according to the method described in claim 2, it is characterized in that,
Crash rate: crash rate pays close attention to failure probability of the software systems within the unit time, is defined asWherein R (t) For reliability function, i.e., there is not the probability to fail in system operation before t moment, and f (t) is failure dense function,
Reliability: the degree of reliability of the attention location system within a period of time, i.e. R (t)；
Mean time to failure: there is the average time of first failure since operation in software, if R (t) is continuous type letter Number, then
Mean time between failures: concern software systems occur failing twice in operation between Mean Time Between Replacement；
Crash rate change rate: the situation that changes with time that fails in software running process is focused on, is passed throughCome into Row calculates, λ (t1) and λ (t2) it is respectively t1And t2The crash rate at moment.
4. the method according to claim 1, wherein the recurrence mould of building reliability index and test feature measurement The process of type specifically includes:
Calculate reliability index；
Determine the citation form of regression model；
Examine influence of the independent variable to reliability index whether significant, retaining influences significant independent variable, and the independent variable is Test feature measurement results；
It is described to examine influence whether significant method of the independent variable to reliability index to include:
If former regression equation is y=β0+β1x1++βi-1xi-1+βixi+βi+1xi+1++βpxp, remove variable xiThe new recurrence obtained afterwards Model is y=β0+β1x1++βi-1xi-1+βi+1xi+1++βpxp, new regression model is referred to as the model that subtracts of former regression model, and title is former to be returned Model is full model, wherein, βiIt is the coefficient of regression model independent variable, p indicates the number of arguments, and x indicates that independent variable, y indicate Dependent variable；
It calculates separately the regression sum of square U of full model and subtracts the regression sum of square U of modeli', to obtain Ui=U-Ui′；? To after the corresponding sum of squares of partial regression of each independent variable, the size that more each factor contributes entire regression effect will be contributed small Person rejects；
If the multiple correlation coefficient of full model square be R2, subtract the multiple correlation coefficient of model square isDefinition
Null hypothesis H0:H1:As null hypothesis H0When being true, test statistics isFor given level of significance α, F is calculated by sample valueiValue, if Fi ≥F1-α(1, n-m-1), then refuse H0, i.e.,It is significantly not zero, this illustrates xiY is had a significant impact, should be added in subtracting model Enter xiMake full model；If Fi< F1-α(1, n-m-1), then receive H0, i.e.,It is significantly zero, this illustrates xiY is influenced not Significantly, x should be rejected in full modeli, make and subtract model；N indicates sample size number, and m indicates the number of arguments.
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