CN102508774A - Modeling method for software reliability growth model based on novel environmental factor function - Google Patents

Abstract

The invention discloses a modeling method for a software reliability growth model based on a novel environmental factor function. The modeling method solves the problem of high fitting and prediction errors due to complicated processing of Logistic curve mathematics, NHPP (non-homogenous Poisson process) software reliability models are adopted, parameters of each model are estimated on the basis of existing failure data, fitting errors are computed, an optimal fitting model at a testing stage is selected, then environmental factors are fit according to empirical data, the novel time-varying environmental factor function is provided, fault detection rate at a running stage is obtained by the aid of the environmental factors and fault detection rate of the testing stage, and the software reliability growth model based on the environmental factors of the novel time function is built. The model built by the aid of the modeling method has high estimation precision and practicality, reliability of a software system can be well predicted, and the problem of high fitting and prediction errors due to complicated processing of Logistic curve mathematics is solved.

Description

Modeling method based on the software reliability growth model of new envirment factor function

Technical field

The present invention relates to the Research of reliability model field, particularly consider test and running environment difference, propose a kind of modeling method of the software reliability growth model based on new envirment factor function.

Background technology

Along with the expansion in software application field and the further raising of functional requirement, the software systems scale increases day by day, and the shared ratio of function that is realized by software in the computer system increases sharply, and the reliability of software becomes one of focus of people's concern.How accurately the reliability of tolerance and predictive software systems is a focus in current software reliability research field.The software reliability modeling is the basis of software reliability engineering; Be intended to provide with the method for statistics the estimated value or the predicted value of software reliability according to software reliability data; The reliability of assessment software is one of software systems reliability assessment and key technology for prediction.

At the test phase of software development, constantly detect and get rid of software fault, improve software reliability, the model of describing this process is called software reliability growth model (Software Reliability Growth Model is called for short SRGM).The software reliability standard that most software reliability growth models is taked all is a testing reliability; Only in the minority document, mentioned operational reliability standard (but list of references J.D.Musa.A theory of software reliability and its application.IEEE Transactions on Software Engineering; 1975; 3 (1): 312～327 with Suresh N; Babu.AJG.Software reliability estimation and optimization; A nonhomogeneous poisson process approach.International Journal of Quality and Reliability Management.1997, (14): 287～300).In the running software stage, the effect of different hardware platforms, operating system and different application software makes that software runtime environment and test environment can not be consistent, and to the software systems predicting of reliability, is to predicting of reliability in user's actual operating condition.The difference of test environment and running environment to the influence of software reliability modeling be mainly reflected in following some:

(1) under the ideal conditions, the test environment of software systems is identical with user's environment for use, and software test moves the sufficiently long time according to user's Operation Profile, the crash rate that obtains tallying with the actual situation.Yet in reality, this is infeasible, expends high surprising in resource with on the time because give the test of operation profile.So in software test procedure; In order to reduce cost and to raise the efficiency; People can adopt various test and testing tool to quicken the inefficacy of software; Test environment can quicken the actual effect process of software, thereby causes estimating the failure intensity of operation phase is pessimistic, also just causes software reliability estimated value and actual value inconsistent.

(2) before the software issue, be difficult to the definition operation profile, promptly the user carries out the probability of a certain operation and generation thereof, and it is different that the distribution that input point is selected in the test phase input domain distributes down with the test section.In addition, different method of testings is variant to the selection of input point, and this will form different test sections, obtains different reliability and estimates numerical value.But (list of references M.H.Chen; A.P.Mathur; V.J.Rego.Effect of Testing Techniques on Software Reliability EstimatesObtained Using Time-Domain Models.IEEE Transactions on Reliability; 1995,44 (1): 97～103).

(3) test phase is different to the method for Reliability Distribution; Such as for the abnormality processing part in the software systems, if according to operation profile software systems are carried out conventionally test, the probability that processing anomalous event part software is performed is very low; And in the actual test; Carry out a lot of test cases and test the abnormality processing module, in this case, the selection under the selection of input point and distribution and the operation profile also is different with distributing.

Therefore, the difference of research test environment and running environment and to the influence of software reliability modeling, the software reliability model of setting up the operation phase is imperative.

At present, the research of consideration test environment and running environment difference mainly is to utilize envirment factor (Environmental factor) to reduce the error of causing for the software reliability estimated accuracy because of the difference of test environment and running environment.This method is to represent envirment factor with a variable, connects at fault detect rate under the running environment and the fault detect rate under the test environment software systems through envirment factor.

Document: X.Zhang; R.J.Daniel; " the Calibrating software reliability models when the test environment does not match the user environment " that H.Pham delivered in 2002 proposed the notion of envirment factor (Environment Factor); It is defined as the ratio of mean failure rate verification and measurement ratio under two kinds of environment, and this ratio is a constant.Document: X.Teng; " the A Software Cost Model for Quantifying the Gain with Considerations of Random Field Environments " that H.Pham delivered in 2004; Document applied environment factor notion is described the difference of test and running environment; It proposes a kind of software reliability model relevant with envirment factor; Suppose that envirment factor is a stochastic variable, the fault detect rate of software systems under running environment is that fault detect rate under the test environment is divided by envirment factor.But they suppose that envirment factor is time-independent constant.Document: it is time dependent that " the Software Reliability Growth Model with Change-Point and Environment Function " that Jing Zhao etc. delivered in 2006 proposes envirment factor; And use Logistic curve fitting envirment factor function:

be N wherein; A,

is undetermined coefficient.But the Logistic curve is not directly perceived, and mathematics manipulation is very complicated, and bigger with the predicated error of the operation phase software reliability model that obtains after the Logistic curve fitting envirment factor.

Summary of the invention

The objective of the invention is to consider the difference of test environment and running environment, solve because Logistic curve mathematics dealing with complicated that the problem that match and predicated error are big proposes a kind of modeling method of the software reliability growth model based on new envirment factor function.

The modeling method of a kind of software reliability growth model based on new envirment factor function of the present invention has following steps:

Step 1, be the fail data of test phase and operation phase with software systems considered repealed data separating;

Step 2, with nonhomogeneous Poisson process (the Non-Homogeneous Poisson Process of several classics; Abbreviation NHPP) a type software reliability model is the basis; Utilize the fail data of test phase; Adopt least square method to estimate the parameter of these models; And the index of correlation R-square that adopts error sum of squares SSE and regression curve equation assesses the performance of these models; Select the best optimum software reliability model of one of them fitting effect, and then obtain the time dependent mean failure rate verification and measurement ratio

of test phase as test phase

Step 3, the time dependent average envirment factor form of definition are confirmed time dependent mean failure rate verification and measurement ratio of operation phase

The time dependent average environment factor

can be expressed as:

$\stackrel{\‾}{k}\left(t\right)=\frac{{\stackrel{\‾}{b}}_{\mathrm{test}}\left(t\right)}{{\stackrel{\‾}{b}}_{\mathrm{field}}\left(t\right)}$

Wherein,

and

represents test and time dependent mean failure rate verification and measurement ratio of operation phase respectively.

Time dependent mean failure rate verification and measurement ratio of operation phase

is:

${\stackrel{\‾}{b}}_{\mathrm{field}}\left(t_i\right)=\frac{\stackrel{\‾}{\mathrm{\λ}}\left(t_i\right)}{a-N\left(t_i\right)}$

Wherein, i=1,2,3 ..., n,

The mean failure rate of the operation phase that expression is discrete; N (t _i) be illustrated in the operation phase from beginning to t _iThe cumulative failure number of actual measurement constantly, a are represented the estimated value of software fault sum.

Step 4, confirm the functional form of new envirment factor:

be A wherein; B; C is three undetermined coefficients, uses least square method to confirm three undetermined coefficients according to time dependent mean failure rate verification and measurement ratio of test phase

and time dependent mean failure rate verification and measurement ratio of operation phase .

Step 5, is at first confirmed the fault detect rate of operation phase

Functional form:

Confirm the failure function a of operation phase then _Field(t): a _Field(t)=(a-m (T)) (1+ α t); Wherein, Functional form for the fault detect rate of resulting test phase model of fit in the step 2; T is the time of software issue; The cumulative failure number of expectation when m (T) issues for software; α representes wrong introducing rate, and a representes the estimative figure that obtains with the optimum whole test phase of model of fit match of test phase and the fail data of operation phase.

Step 6, definite following based on the software reliability growth model of new envirment factor function:

$m\left(t\right)=(a-m\left(T\right))(1+\mathrm{\αt})(1-{\left(\frac{A+{\mathrm{Ce}}^{\mathrm{Bt}}}{A+C}\right)}^{-\frac{b}{B+C}}),t>0$

Wherein, b representes the model parameter of the optimal fitting model of the test phase that step 2 obtains.

Advantage of the present invention and good effect are: (1) software reliability modeling method of the present invention is considered the drawback of present software reliability modeling assumption; Time dependent envirment factor is incorporated in the software reliability modeling, connects at fault detect rate under the running environment and the fault detect rate under the test environment software systems through envirment factor; (2) software reliability modeling method of the present invention proposes the envirment factor of new function form, and directly perceived being prone to handled, and in practical application, can directly use according to empirical data in the past; (3) software reliability modeling method of the present invention is different from the software reliability model of test phase in the past, foundation be the model of operation phase, have very high estimated accuracy, practicality, reliability that can well predictive software systems.

Description of drawings

Fig. 1 is the schematic flow sheet of the whole modeling method of the present invention;

Fig. 2 is the curve synoptic diagram of each software reliability model of embodiment of the invention selection to the test phase data fitting;

Fig. 3 is the envirment factor matched curve of new function form;

Fig. 4 is the matched curve of each model to the operation phase data;

Fig. 5 is the assessment curve of each model prediction ability.

Embodiment

To combine accompanying drawing and embodiment that the present invention is done further detailed description below.

The new envirment factor function that the present invention proposes changes in time, has set up the method for operation phase software reliability growth model.Adopt NHPP class software reliability model hypothesis; On existing fail data, estimate the parameter of each model, calculate error of fitting, select the optimum fitness model of test phase; Data fitting envirment factor rule of thumb then; Propose a kind of envirment factor of new time dependent functional form, obtain the fault detect rate of operation phase through the fault detect rate of envirment factor and test phase, foundation is based on the software reliability model of the envirment factor of the new function of time; Realize better reliability match and predictive ability, have very high capability of fitting and predictive ability.

Be background with the NHPP class model in the embodiment of the invention, adopt following assumed condition:

(1) the accumulative total inefficacy function m (t) to time t satisfies Poisson process; And suppose that this accumulative total function that lost efficacy is the nondecreasing function of bounded, and

is limited failure model;

(2) for the t of finite time sampling arbitrarily ₁＜t ₂＜...＜t _n, at each separation time interval [t ₀=0, t ₁), (t ₁, t ₂) ... (t _i, t _I+1) ... (t _N-1, t _n] interior detected error number (k ₁, k ₂... K _n) be separate;

(3) in the failure intensity of software and the software still the undetected failure sum be directly proportional;

(4) the running software mode is identical with the reliability prediction mode;

(5) each wrong chance that takes place is identical, and each wrong order of severity is identical;

Losing efficacy when (6) mistake is to be detected is independently.

Note N (t) is the cumulative failure number till the t moment, and establishes m (0)=m ₀, m (∞)=a (t), m ₀It is a unknown constant.With b (t) expression fault detect rate, the number of the appearance of in (t, t+ Δ t), losing efficacy is directly proportional with the residue failure number (a (t)-m (t)) in the t moment, that is:

m(t+Δt)-m(t)＝b(t)·(a(t)-m(t))·Δt (1)

Make Δ t → 0:

m′(t)＝a(t)b(t)-b(t)m′(t) (2)

The general solution of following formula is:

$m\left(t\right)=e^{-{\&Integral;}_0^{t}b\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;}}\mathrm{dt}[{\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="HDA0000103162700000021.png"\; state="\{\{state\}\}">m</figure-callout>}}_0+{\&Integral;}_0^{t}a\left(\mathrm{\&tau;}\right)b\left(\mathrm{\&tau;}\right)e^{{\&Integral;}_0^{\mathrm{\&tau;}}b\left(v\right)\mathrm{dv}}\mathrm{d\&tau;}]---\left(3\right)$

Many NHPP class software reliability growth models all are according to actual conditions, revise above assumed condition, the accumulative total function m (t) that lost efficacy of deriving out of the process above utilizing.

The modeling method of software reliability growth model of the present invention is specifically as shown in Figure 1, may further comprise the steps:

Step 1, analyzing software system considered repealed data, the fail data of discrete testing stage and operation phase;

Use the fail data of existing software systems fail data discrete testing stage and operation phase.Existing software systems fail data is seen table 1 [list of references: M.Lyu, Ed. be disclosed Handbook Software Reliability Engineering.New York:McGraw-Hill.P79～109 in 1996].The accumulated time (Cumulative Time Between Failure is abbreviated as Cumulative TBF in the table) of having listed 136 faults (Fault) in the table and having occurred.From the 122nd lost efficacy to the time interval the 123rd inefficacy clearly.After the 123rd inefficacy, the out-of-service time is very big at interval, and considerably beyond the interval of the out-of-service time before the 122nd inefficacy, this reliability that is indicating software systems increases, and it is stable that system becomes.So, in the software reliability Modeling Method, select the data of preceding 122 fail datas as test phase, be used for the estimation model parameter, calculate error of fitting, and select the model of fit of test phase; Remaining data are as the data of operation phase, are used for the predictive ability of assessment models.

Table 1 thrashing data

Step 2, be the basis with the NHPP class software reliability model of several classics; Utilize the fail data of test phase; Adopt least square method to estimate the parameter of these models; And the performance of the index of correlation R-square assessment software reliability model of employing error sum of squares SSE and regression curve equation; Select the best software reliability model of one of them fitting effect, and then obtain the time dependent mean failure rate verification and measurement ratio

of test phase as test phase

To the test phase fail data, adopt least square method Estimation Software reliability model parameter, the performance that the index of correlation R-square of employing error sum of squares (the Sum of Squared Errors) SSE and regression curve equation comes the assessment reliability model.

SSE is used for describing the observed reading of cumulative failure number and the distance between the predicted value, and SSE is defined as:

$\mathrm{SSE}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-m\left(t_i\right))}^2---\left(4\right)$

R-square is defined as:

$R-\mathrm{square}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(\hat{m}\left(t_i\right)-\stackrel{\&OverBar;}{y})}^2}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-\stackrel{\&OverBar;}{y})}^2}---\left(5\right)$

In (4), (5) formula, i=1,2,3 ..., n, n represent the quantity of the concentrated inefficacy sample of fail data,

Be illustrated in t _iThe errors that moment model assessment obtains, y _iBe illustrated in t _iThe factual error number that constantly observes;

Expression is from t ₀To t _iThe mean value of the factual error number that constantly observes can be expressed as:

$\stackrel{\&OverBar;}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i---\left(6\right)$

The value of SSE is more little, and the error of curve fitting is more little; The value of R-square is more near 1, curve fitting good more.

The parameter value of the model name that can select in the software test stage, model tormulation formula, estimation, the result of calculation of SSE and R-square is as shown in table 2.

The estimates of parameters of each model of table 2 and capability of fitting

Fig. 2 simulation result shows that the P-N-Z model is at test phase, and especially at preceding 20000 seconds, fitting effect was very good; Though the expectation cumulative failure number of all models is all greater than actual value after 350000 seconds; Pessimistic estimation has appearred; But the SSE that can find out whole test phase P-N-Z model from table 2 is minimum, and R-square explains that near 1 the error of P-N-Z model is minimum, capability of fitting is best.So select the P-N-Z model at the model of fit of test phase in embodiments of the present invention.Test phase, the fault detect rate of P-N-Z model

is:

${\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)=\frac{b}{1+{\mathrm{\&beta;e}}^{-\mathrm{bt}}}=\frac{0.00005}{1+0.002\&times;e^{-0.00005t}}---\left(7\right)$

Wherein, b representes the parameter value of selected optimal fitting model in the step 2, the parameter value b=0.00005 of P-N-Z model in the embodiment of the invention.At test phase, when fault detect rate was reduced to a certain degree, software had certain reliability and just can issue.Growth along with the test duration; T increases gradually, and

gets

Step 3, confirm time dependent average environment factor form, confirm time dependent mean failure rate verification and measurement ratio of operation phase

Definition environment factor k (t) is:

$k\left(t\right)=\frac{b_{\mathrm{test}}\left(t\right)}{b_{\mathrm{field}}\left(t\right)}---\left(8\right)$

Wherein, b _Test(t) and b _Field(t) represent t test phase and the fault detect rate of operation phase constantly respectively.Because measured data disperses, the so time dependent average environment factor

can be expressed as

$\stackrel{\&OverBar;}{k}\left(t\right)=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{{\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)}---\left(9\right)$

Wherein, I=1; 2; 3 ... N,

and

represent test and time dependent mean failure rate verification and measurement ratio of operation phase respectively.

Suppose that the software test stage finishes in time T, promptly T is the issuing time of software, after this gets into the on-the-spot operation phase of software.Software systems can be tried to achieve through following formula at the crash rate λ of operation phase (t):

λ(t)＝b _field(t)×(a-m(t))(t＞T) (10)

Wherein, a representes the estimative figure that obtains with the whole test phase of P-N-Z model fitting and the fail data of operation phase, and the embodiment of the invention uses the P-N-Z model to estimate a=140.4, the expectation failure number that m (t) expression is accumulated from the operation phase to t constantly.

With N (t _i) represent that the operation phase begins to t _iThe cumulative failure number of actual measurement constantly, the mean failure rate of operation phase

Can be expressed as:

$\stackrel{\&OverBar;}{\mathrm{\&lambda;}}\left(t_i\right)=\frac{N\left(t_i\right)}{t_i}---\left(11\right)$

With the m (t) in (10) formula with N (t _i) replace, λ (t) uses

Replace, so time dependent mean failure rate verification and measurement ratio of operation phase

Can be expressed as:

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t_i\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}\left(t_i\right)}{a-N\left(t_i\right)}---(12-1)$

Work as t _i=t is during the moment, and formula (12-1) can be expressed as:

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}\left(t\right)}{a-N\left(t\right)}---(12-2)$

Step 4, according to actual conditions and the assumed condition of NHPP class software reliability model is set, confirm the functional form of envirment factor.

Analysis to envirment factor is following:

1, when fault detect rate is reduced to a certain degree, software has certain reliability just can be issued, so the fault detect rate of test phase is decreasing function or is tending towards a constant when test phase finishes; The fault detect rate of operation phase

is determined by formula (12-2); It is relevant with factors such as environment for use, operating personnel's custom, software systems length working time, functional module frequencies of utilization;

changes is uncertain, possibly be that increasing function also possibly be subtraction function or constant.No matter be what situation, envirment factor all should be time dependent function, and its trend is perhaps successively decreasing of increasing progressively in time;

2, in the reasonable model of already present fitting effect; Some predicted results is relatively more optimistic; Such as the G-0 model; The cumulative failure number of estimating lacks than the cumulative actual failure number, and the fault detect rate

that makes the operation phase of calculating is a negative; Some predicted results is relatively more pessimistic; Like the LV model, the fault detect rate

that makes the operation phase of calculating is a positive number.Both of these case makes that envirment factor

value might be on the occasion of being negative value.

According to above analysis, the theoretical curve expression formula of the definition environment factor is:

${\stackrel{\&OverBar;}{k}}_{\mathrm{new}}\left(t\right)=A\&times;e^{-\mathrm{Bt}}+C---\left(13\right)$

Wherein, A, B, C are undetermined coefficient, it represents meaning following:

(1) uses e ^-BtThe increasing or decreasing trend of match envirment factor.When B parameter＞0, the expression envirment factor is successively decreased in time; When B＜0, the expression envirment factor increases progressively in time.And the size of B is represented the speed of environment factor variations.

(2) represent the ratio of environment factor variations with A.

(3), add C and be the adjustment coefficient according to analyzing 2.When A＞0, A * e ^-Bt＞0; When A＜0, A * e ^-Bt＜0, adjustment coefficient C can realize making the value of discrete envirment factor to have positive number that negative is also arranged.

According to the previous step to get the

and computing discrete values of environmental factors.The initial value of the theoretical curve of envirment factor is:

(1) works as t=0; Be that software systems get into the operation phase,

(2) as t → t _FinalThe time, promptly arrive the final stage of moving, t _FinalThe final moment of expression operation phase.

According to top two conditions, A is set, B, the initial value of C parameter calculates A with least square method, B, C.The functional form that obtains new envirment factor is:

${\stackrel{\&OverBar;}{k}}_{\mathrm{new}}\left(t\right)=A\&times;e^{-\mathrm{Bt}}+C=3.7\&times;e^{-0.000036t}+0.01---\left(14\right)$

Be coefficient A=3.7, B=0.000036, C=0.01; Error of fitting is SSE=0.0098.The curve of the envirment factor shown in the formula (14) is as shown in Figure 3.

With Logistic function match envirment factor:

${\stackrel{\&OverBar;}{k}}_{\log i}\left(t\right)=\frac{N}{1+A\&times;e^{-\&PartialD;t}}=\frac{15.1}{1+5.1\&times;e^{0.000032t}}---\left(15\right)$

Be coefficient N=15.1; A=5.1,

error of fitting SSE=0.01.The error of fitting of the envirment factor that use the inventive method obtains is littler than the error of fitting of using Logistic function match envirment factor.

Step 5, try to achieve the functional form of operation phase fault detect rate, and calculate the primary fault number of operation phase;

According to the calculating in the step 2; Test phase, the fault detect rate of P-N-Z model

1, utilize new envirment factor functional form, the fault detect rate of operation phase is:

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{A\&times;e^{-\mathrm{Bt}}+C}=\frac{0.00005}{3.7\&times;e^{-0.000036t}+0.01}---\left(16\right)$

2, utilize the Logistic functional form, the fault detect rate of operation phase does

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{N}(1+A\&times;e^{-\&PartialD;t})=\frac{0.00005}{15.1}\&times;(1+5.1\&times;e^{0.000032t})---\left(17\right)$

The failure function a of operation phase _Field(t) be:

a _field(t)＝(a-m(T))(1+αt) (18)

Wherein, T is the time of software issue, the cumulative failure number of expectation when m (T) issues for software.α representes wrong introducing rate.A representes the estimative figure that obtains with the optimum whole test phase of model of fit match of test phase and the fail data of operation phase.

Step 6, definite software reliability growth model based on new envirment factor function.The software reliability growth model of operation phase is:

m _field(t)＝a _field(1-e ^-B*(t)) (19)

Wherein, $B*\left(t\right)={\&Integral;}_0^t{b}_{\mathrm{Field}}\left(t\right)\mathrm{Dt}.$

Formula (16) and formula (18) substitution formula (19) can be obtained the software reliability model based on new envirment factor function:

$m\left(t\right)=(a-m\left(T\right))(1+\mathrm{\&alpha;t})(1-{\left(\frac{A+{\mathrm{Ce}}^{\mathrm{Bt}}}{A+C}\right)}^{-\frac{b}{B+C}}),t>0---\left(20\right)$

Formula (17) and formula (18) substitution formula (19) can be obtained the software reliability model that envirment factor is the Logistic functional form:

$m\left(t\right)=(a-m\left(T\right))(1+\mathrm{\&alpha;t})(1-\exp (-(\frac{b}{N}t+\frac{\mathrm{bA}}{N\&PartialD;}(1-e^{-\&PartialD;t})))),t>0---\left(21\right)$

If make M=(a-m (T)),

formula (20) so can turn to:

m(t)＝M(1+αt)(1-(X+XCe ^Bt) ^-Z)t＞0 (22)

If make

so formula (21) can turn to:

$m\left(t\right)=M(1+\mathrm{\&alpha;t})(1-\exp (-(\mathrm{Gt}+H(1-e^{-\&PartialD;t})))),t>0---\left(23\right)$

Model shown in the formula (22) that the present invention is obtained compares with the software reliability model that suc as formula the envirment factor shown in (23) is the Logistic functional form: the first half of formula (22) is a linear change in time, and latter half is that index changes the binomial form with constant; Relative formula (23), the mathematics manipulation more complicated of formula (22) comprises the part of linear change and the part of index variation in time in the speed of index variation.This shows that the model form that the present invention is based on new envirment factor function foundation is directly perceived, mathematics manipulation is easy, is easier to use actual.

RE (Relative Error) is used for the predictive ability of computation model, and RE is more near 0, and the predictive ability of curve is good more, and RE is defined as:

$\mathrm{RE}=\frac{m\left(t_i\right)-y_i}{y_i}---\left(24\right)$

Wherein, i=1,2,3 ..., n, m (t _i) represent t _iThe estimated value of inefficacy cumulative number constantly, y _iRepresent t _iThe measured value of inefficacy cumulative number constantly.Use the capability of fitting and the predictive ability of the operation phase fail data testing model of software systems.See table 3 in each model fitting ability of operation phase and predictive ability data, wherein the L-F model is for using the software reliability model of Logistic function as envirment factor.

Each model prediction ability of table 3 relatively

Data from table 3 can find out that several kinds of model contrasts are in the whole service stage; The SSE=57.3301 of the model that employing the inventive method obtains, R-square=0.8465, the value of SSE is minimum; The value of R-square is near 1, and it is minimum just to adopt the inventive method to obtain the error of model curve match, curve fitting best; Be that predicated error is minimum in the listed model, the model that anticipation trend is best.

As shown in Figure 4, be 8 kinds of results that model carries out emulation in the his-and-hers watches 3, model of the present invention is obvious in the predictive ability in whole service stage, and particularly model almost overlaps with measured data between the 80000th and 85000; Comparatively speaking, other models can only be predicted the general trend of actual measurement cumulative failure number, and the model prediction result who has is relatively optimistic, and the model estimated result that has is relatively pessimistic; Observe the L-F model, though that it predicts the outcome is well more a lot of than the modelling effect of the environment for use factor not, with measured data at a distance of very big, the model that relative the inventive method obtains, or some is inferior.Be illustrated in figure 5 as in the his-and-hers watches 38 kinds of models and carry out the predictive ability assessment curve display that emulation obtains, the RE curve of the model that the present invention obtains and is to approach 0 most all the time almost in 0.02, levels off to 0 gradually in the earthquake; Comparatively speaking, the RE curvilinear motion of other models is very big, does not have convergent trend, like the G-O model, and Yamada Exponential model, perhaps bigger always, like Delayed S-Shaped model; Observe the L-F model, its RE curve nearly all outside 0.02, does not converge to 0 trend.

Software reliability modeling process of the present invention can be used in the different fail datas; And the empirical data that lost efficacy according to software systems; Utilize the functional form of envirment factor of the present invention; Can calculate the fault detect rate of operation phase, thereby set up the software reliability growth model of operation phase.Like data in the table 3 and Fig. 4, the simulation result of Fig. 5 shows that the operation phase software reliability growth model of using the functional form foundation of envirment factor of the present invention has good capability of fitting, and the new envirment factor functional form that the present invention proposes is feasible; Contrast model of the present invention and L-F model, the error of new model is littler, and capability of fitting is stronger; The RE of new model more approaches 0, and good precision of prediction is promptly arranged.

Claims (2)

1. the modeling method based on the software reliability growth model of new envirment factor function is characterized in that this modeling method comprises the steps:

Step 1, the software systems fail data is separated into the fail data of test phase and the fail data of operation phase;

Step 2, selection nonhomogeneous Poisson process class software reliability model; Utilize the fail data of test phase to adopt least square method to estimate the parameter of selected each software reliability model; And the index of correlation R-square that adopts error sum of squares SSE and regression curve equation assesses the performance of selected each software reliability model; Select the best optimum software reliability model of one of them fitting effect, and then obtain the time dependent mean failure rate verification and measurement ratio

of test phase as test phase

Step 3, the time dependent average envirment factor form of definition are confirmed time dependent mean failure rate verification and measurement ratio of operation phase

The time dependent average environment factor

is:

$\stackrel{\&OverBar;}{k}\left(t\right)=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{{\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)}---\left(1\right)$

Wherein,

and

represents test and time dependent mean failure rate verification and measurement ratio of operation phase respectively;

Time dependent mean failure rate verification and measurement ratio of operation phase

is:

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t_i\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}\left(t_i\right)}{a-N\left(t_i\right)}---\left(2\right)$

Work as t _i=t is during the moment, and formula (2) is expressed as:

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&lambda;}}\left(t\right)}{a-N\left(t\right)}---\left(3\right)$

Wherein, i=1,2,3 ..., n, N (t _i) be illustrated in the cumulative failure number of operation phase from beginning to survey constantly to ti; A representes the estimation of software fault sum;

The mean failure rate of expression operation phase,

Step 4, confirm that the functional form of new envirment factor

is following:

${\stackrel{\&OverBar;}{k}}_{\mathrm{new}}\left(t\right)=A\&times;e^{-\mathrm{Bt}}+C---\left(4\right)$

Wherein, coefficient A representes the ratio of environment factor variations; Coefficient B is represented the speed of environment factor variations; e ^-BtThe increasing or decreasing trend that is used for the match envirment factor, when B＞0, expression envirment factor t is in time successively decreased, and when B＜0, expression envirment factor t in time increases progressively; Coefficient C representes to adjust coefficient, makes the value of envirment factor have positive number that negative is also arranged;

According to

value that obtains in

value that obtains in the step 2 and the step 3; On the software systems fail data collection of step 1, use least square method to estimate three undetermined coefficient A, B and C;

Step 5, at first; Functional form in conjunction with the new envirment factor that obtains; Confirm the function expression of the fault detect rate

of operation phase, obtain according to step 3 Chinese style (1):

${\stackrel{\&OverBar;}{b}}_{\mathrm{field}}\left(t\right)=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{{\stackrel{\&OverBar;}{k}}_{\mathrm{new}}\left(t\right)}=\frac{{\stackrel{\&OverBar;}{b}}_{\mathrm{test}}\left(t\right)}{A\&times;e^{-\mathrm{Bt}}+C}---\left(5\right)$

Confirm the failure function a of operation phase then _Field(t):

a _field(t)＝(a-m(T))(1+αt) (6)

Wherein, T is the time of software issue, the cumulative failure number of expectation when m (T) issues for software, and α representes wrong introducing rate; Step 6, definite software reliability growth model based on new envirment factor function:

$m\left(t\right)=(a-m\left(T\right))(1+\mathrm{\&alpha;t})(1-{\left(\frac{A+{\mathrm{Ce}}^{\mathrm{Bt}}}{A+C}\right)}^{-\frac{b}{B+C}}),t>0---\left(7\right)$

Wherein, b representes the model parameter of the optimum software reliability model of the test phase that step 2 obtains.

2. the modeling method of a kind of software reliability growth model based on new envirment factor function according to claim 1 is characterized in that, the coefficient that the use least square method described in the step 4 is confirmed is: A=3.7, B=0.000036, C=0.01.

Images