KR20200107392A - A method of predicting software failure time based on nonlinear regression model and a computer readable medium thereof - Google Patents

Abstract

According to the present invention, disclosed are a method of predicting a software failure time based on a nonlinear regression model, and a computer-readable recording medium. The method includes the steps of: allowing a trend certification part to predict a software failure time by using a nonlinear regression model; and allowing a failure time analysis part to determine an optimal parameter statistic model for the predicted software failure time by using a determination coefficient and a mean square error. According to the present invention, in fields of software system design and software reliability, software developers and managers can accurately predict and consider an increase in necessary information for data censorship, thereby quickly and accurately analyzing and predicting a software failure time, which can lead to an improvement in software stability.

Description

A method of predicting software failure time based on nonlinear regression model and a computer readable medium thereof

The present invention relates to a method of predicting software failure time, and in particular, a nonlinear regression model that can accurately predict future failure time by examining software failure time using a nonlinear regression model, and determining a model with a high coefficient of determination and a low mean square error. A method for predicting software failure time based on a regression model and a computer-readable recording medium.

In general, a repairable system means that when a failure occurs, the system can be operated by repairing the defective part or replacing the entire system.

Most of today's systems consist of complex repairable systems that are difficult to analyze.

However, if the system reliability can be accurately predicted by introducing a systematic analysis method, it will be helpful to establish an efficient maintenance policy.

The main concern in repairable systems is to detect failure patterns, and is said to have a constant trend when the inter-failures time changes according to a certain pattern.

If, as a monotonic trend, the failure interval time becomes longer, it means that reliability is improved. Conversely, if the failure interval time becomes shorter, it means that reliability is deteriorated.

In addition, there are cases in which the periodicity of the failure interval time becomes shorter and longer, or the bath-tub curve shape becomes constant and longer after the failure interval time is shorter.

There are two methods that are practically used when analyzing failure patterns, a graphical method and a statistical test method.

Illustrative methods allow you to identify overall trends in the data by graphically showing observed failure data.

For example, showing the cumulative number of failures according to the failure occurrence time provides simple and very useful information.

At this time, if the shape shown during the observation time is linear, it means that the failure rate is constant.

If the failure interval time data are independent and show the form of an exponential distribution, it means that the Renewal process or the Homogeneous Poisson Process is suitable.

The homogeneous Poisson process is the simplest statistical model that can explain the occurrence of failures in a repairable system, and assumes minimal repair.

Here, the minimum repair means repairing the system to the state before the failure when a system failure occurs.

Simple methods of distinguishing whether or not a homogeneous Poisson process is performed include a method showing the cumulative failure rate for each failure occurrence time and a Duane plot (a diagram of log-converted failure time and log-converted accumulated failure rate).

If the points shown in both methods have linearity, it can be determined that the homogeneous Poisson process is a suitable model.

However, since the homogeneous Poisson process cannot explain the initial failure period of the entire life cycle of the repairable system and the wear failure period that deteriorates reliability, the entire life cycle of the system is recommended to use the Nonhomogeneous Poisson Process. It is common.

Here, the non-homogeneous Poisson process refers to a parametric statistical model that has a constant trend because the failure rate is not constant, unlike a homogeneous Poisson process that has a constant failure rate.

On the other hand, the incidence rate of failure of various software is constant or has a monotonically increasing or monotonically decreasing pattern.

Recently, various trend analysis has been developed for data analysis of the software reliability model.

Methods of trend analysis include arithmetic mean test and Laplace trend test.

However, computer system errors due to software failure can cause enormous losses in our society.

Therefore, software stability is an important issue in the software development process, and it must meet the user's requirements and test costs.

To reduce the cost of software variability and reliability, it is necessary to know in advance the cost of software testing (debugging) efficiently.

Therefore, a software development process that considers software reliability cost and failure time is essential, and it is necessary to develop a model that can improve quality by evaluating the defect contents of software products.

So far, many software stability models have been proposed, and some of these models to explain software failure phenomena are based on non-homogeneous Poisson processes.

In fact, these models are quite effective in canceling the error detection process at the rate of error detection over time, but they assume that whenever an error occurs, the error is immediately removed so no new problem arises, and this problem is usually perfect for debugging. It is called (Debugging).

However, the trend analysis methods already developed for data analysis of the software reliability model in the related art can only provide information on the outline contents, and have a limitation in not being able to analyze the intermediate cut failure time and the predicted failure time.

In addition, trend information of a repairable system is used to determine the preventive maintenance cycle and the number of maintenance of the preventive maintenance policy.

Test methods for obtaining such trend information include TTT plot (Total Time on Test plot), Nelson-Aalen plot, military handbook test, Laplace test, Lewis-Robinson (LR) test, and Pair-wise Comparison Nonparametric test (PCNT) test. Is being used.

However, most of the conventional trend test methods have a limitation in that they provide only fragmentary information about the system as a method for simply testing the presence or absence of a trend.

Accordingly, the present inventor has come to invent a software failure time prediction method capable of evaluating the defect contents of a software product in consideration of software reliability cost and failure time, and quickly and accurately analyzing and predicting the software failure time.

JP 1996-030493 A

An object of the present invention is based on a nonlinear regression model capable of predicting future failure times by examining the cutoff time and prediction time using a nonlinear regression model with different error periods, and determining a model with a high coefficient of determination and a low mean square error. It is to provide a method of predicting software failure time.

Another object of the present invention is to provide a computer-readable recording medium recording a program for executing a method of predicting software failure time based on a nonlinear regression model in a computer in order to achieve the above object.

The method for predicting software failure time based on a nonlinear regression model of the present invention for achieving the above object includes: predicting a software failure time by using a nonlinear regression model by a trend test unit; And determining, by a failure time analysis unit, an optimal parameter statistical model for the predicted software failure time using a determination coefficient and a mean square error. It characterized in that it comprises a.

A method for predicting software failure time based on a nonlinear regression model of the present invention for achieving the above object includes: (a) verifying the validity of the data using software failure time data collected by a trend test analysis unit; (b) receiving, by a parameter estimate calculation unit, the verified failure time data and calculating a parameter estimate for a nonlinear regression model; (c) calculating, by an optimal model reference calculation unit, a determination coefficient and a mean square error for determining a failure time prediction model; (d) predicting failure time data by analyzing a future failure time with respect to an actual value by receiving the calculated determination coefficient and the mean square error calculated by a failure time prediction unit; And (e) determining an optimal parameter statistical model by analyzing the predicted failure time data by an optimal model determination unit. It characterized in that it comprises a.

A computer-readable recording medium of a method for predicting software failure time based on a nonlinear regression model of the present invention for achieving the above other object includes: predicting a software failure time by using a nonlinear regression model by a trend test unit; And determining, by a failure time analysis unit, an optimal parameter statistical model for the predicted software failure time using a determination coefficient and a mean square error. It characterized in that it comprises a.

The computer-readable recording medium of the method for predicting software failure time based on a nonlinear regression model of the present invention for achieving the above other object includes: (a) verifying the validity of the data with software failure time data collected by a trend test analysis unit; (b) receiving, by a parameter estimate calculation unit, the verified failure time data and calculating a parameter estimate for a nonlinear regression model; (c) calculating, by an optimal model reference calculation unit, a determination coefficient and a mean square error for determining a failure time prediction model; (d) predicting failure time data by analyzing a future failure time with respect to an actual value by receiving the calculated determination coefficient and the mean square error calculated by a failure time prediction unit; And (e) determining an optimal parameter statistical model by analyzing the predicted failure time data by an optimal model determination unit. It characterized in that it comprises a.

Details of other embodiments are included in "Specific contents for carrying out the invention" and the attached "Drawings".

Advantages and/or features of the present invention, and a method of achieving them will become apparent with reference to various embodiments described below in detail together with the accompanying drawings.

However, the present invention is not limited only to the configuration of each embodiment disclosed below, but may be implemented in various different forms, and only each embodiment disclosed in the present specification makes the posting of the present invention complete. It should be understood that the present invention is provided to completely inform the scope of the present invention to those of ordinary skill in the art, and the present invention is only defined by the scope of each claim in the claims.

According to the present invention, in the field of software system design and software reliability, software developers and operators accurately predict and consider the increase in information required to inspect data, so that software failure time can be quickly and accurately analyzed and predicted. Can improve software stability.

1 is a block diagram of a prediction apparatus for implementing a method of predicting a software failure time based on a nonlinear regression model of the present invention.
FIG. 2 is a flowchart illustrating an operation of a method for predicting a software failure time based on a nonlinear regression model according to an embodiment of the present invention.
3 is a flowchart for explaining the operation of a method for predicting a software failure time based on a nonlinear regression model according to another embodiment of the present invention.
FIG. 4 is a table showing software failure time data to be validated in step S210 of the method for predicting software failure time shown in FIG. 3.
FIG. 5 is a graph of a Laplace trend test analysis used in step S210 of the method for predicting software failure time shown in FIG. 3.
6 is a table showing parameter estimates of each of the nonlinear regression models calculated in step S220 of the software failure time prediction method shown in FIG. 3.
FIG. 7 is a table showing coefficients of determination and mean square errors of each of the nonlinear regression models calculated in step S230 of the method for predicting software failure time illustrated in FIG. 3.
FIG. 8 is a graph for explaining a change in the predicted failure time compared to the number of failures (1 to 30) by the method of predicting the software failure time shown in FIG. 3 by comparing each nonlinear regression model with an actual value.
9 is a table for explaining by comparing each nonlinear regression model with respect to basic statistical information on the number of failures (1 to 30) predicted by the method for predicting a software failure time shown in FIG. 3.
FIG. 10 is a graph for explaining a change in the predicted failure time compared to the number of failures 31 to 40 by the method of predicting the software failure time shown in FIG. 3 by comparing each of the nonlinear regression models.
11 is a table for explaining by comparing each of the nonlinear regression models with respect to basic statistical information about the number of failures 31 to 40 predicted by the method for predicting a software failure time illustrated in FIG. 3.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Before describing the present invention in detail, terms and words used in the present specification are not to be interpreted as being unconditionally limited to their usual or dictionary meanings, and in order for the inventors of the present invention to describe their invention in the best way The concept of various terms can be appropriately defined and used.

Furthermore, it should be understood that these terms or words should be interpreted as meanings and concepts consistent with the technical idea of the present invention.

That is, the terms used in the present specification are only used to describe a preferred embodiment of the present invention, and are not intended to specifically limit the content of the present invention.

It should be understood that these terms are terms defined in consideration of various possibilities of the present invention.

In addition, in the present specification, a singular expression may include a plurality of expressions unless clearly indicated in a different meaning in the context.

In addition, it should be noted that even if it is expressed in a similar plural form, it may include a singular meaning.

Throughout the present specification, when a component is described as "including" another component, it does not exclude any other component, but further includes any other component unless otherwise indicated. It could mean you can do it.

Furthermore, when a component is described as "existing inside or being connected and installed" of another component, the component may be directly connected to or installed in contact with the other component.

In addition, it may be installed spaced apart by a certain distance, and in the case of installation spaced apart from each other by a certain distance, a third component or means for fixing or connecting the component to other components may exist. .

Meanwhile, it should be understood that the description of the third component or means may be omitted.

On the other hand, when a component is described as being "directly connected" to another component or "directly connected", it should be understood that there is no third component or means.

Likewise, other expressions describing the relationship between each component, such as "between" and "directly between", or "neighbor to" and "directly neighbor to" have the same effect. Should be interpreted as.

In addition, in the present specification, terms such as “one side”, “the other side”, “one side”, “the other side”, “first”, and “second” refer to a component in which one component is different for one component. It is used to make it clearly distinct from the element.

However, it should be noted that the meaning of the corresponding component is not limitedly used by such terms.

In addition, in the present specification, terms related to positions such as "upper", "lower", "left", and "right", if used, should be understood as indicating a relative position in the drawing with respect to the corresponding component.

In addition, these position-related terms should not be understood as referring to absolute positions unless absolute positions are specified for their positions.

Moreover, in the specification of the present invention, terms such as "... unit", "... group", "module", "device", if used, mean a unit capable of processing one or more functions or operations.

It should be noted that this can be implemented in hardware or software, or a combination of hardware and software.

In the drawings attached to the present specification, the size, position, and coupling relationship of each component constituting the present invention are partially exaggerated, reduced, or omitted in order to sufficiently clearly convey the spirit of the present invention or for convenience of description. It may have been described, and therefore its proportion or scale may not be exact.

In addition, in the following description of the present invention, a detailed description of a configuration determined to unnecessarily obscure the subject matter of the present invention, for example, a known technology including the prior art may be omitted.

1 is a block diagram of a prediction apparatus for implementing a method for predicting a software failure time based on a nonlinear regression model of the present invention, and includes a trend test unit 100 and a failure time analysis unit 200.

The trend test unit 100 includes a trend test analysis unit 110, a parameter estimate calculation unit 120, and an optimal model reference calculation unit 130, and the failure time analysis unit 200 is a failure time prediction unit 210 And an optimum model determination unit 220.

FIG. 2 is a flowchart illustrating an operation of a method for predicting a software failure time based on a nonlinear regression model according to an embodiment of the present invention.

An operation of a method for predicting a software failure time based on a nonlinear regression model according to an embodiment of the present invention will be schematically described below with reference to FIGS. 1 and 2.

The present invention analyzes and predicts a future failure time by using the following algorithm with failure time data previously collected using an optimal growth regression model.

That is, the trend test unit 100 predicts the software failure time using the nonlinear regression model (S110).

The failure time analysis unit 200 determines an optimal parameter statistical model for the predicted software failure time using the determination coefficient and the mean squared error (S120).

3 is a flowchart for explaining the operation of a method for predicting a software failure time based on a nonlinear regression model according to another embodiment of the present invention.

An operation of a method for predicting a software failure time based on a nonlinear regression model according to another embodiment of the present invention will be schematically described below with reference to FIGS. 1 and 3.

The present invention analyzes and predicts a future failure time by using the following algorithm with failure time data previously collected using an optimal growth regression model.

First, the validity of the data is verified through a Laplace trend test analysis with the software failure time data collected by the trend test analysis unit 110 in the trend test unit 100 (S210).

,

,

)를 계산한다(S220).The parameter estimate calculation unit 120 receives the failure time data for which the validity of the data is verified from the trend test analysis unit 110, and the parameter estimate for the nonlinear regression model (

,

,

) Is calculated (S220).

및 평균 제곱 오차(MSE)를 계산한다(S230). Determination coefficient for the optimal model reference calculation unit 130 to determine an efficient failure time prediction model

And a mean squared error (MSE) is calculated (S230).

및 평균 제곱 오차(MSE)를 인가받아 실제 값에 대한 장래의 고장 시간을 분석하여 고장 시간 데이터를 예측한다(S240). After that, the failure time prediction unit 210 in the failure time analysis unit 200 calculates the calculation determination coefficient from the optimal model reference calculation unit 130

And a mean square error (MSE) is applied to analyze a future failure time with respect to an actual value to predict failure time data (S240).

The optimal model determination unit 220 analyzes the failure time data predicted from the trend test analysis unit 110 to determine an optimal parameter statistical model (S250).

FIG. 4 is a table showing software failure time data to be validated in step S210 of the method for predicting software failure time shown in FIG. 3.

FIG. 5 is a graph of a Laplace trend test analysis used in step S210 of the method for predicting software failure time shown in FIG. 3.

6 is a table showing parameter estimates of each of the nonlinear regression models calculated in step S220 of the software failure time prediction method shown in FIG. 3.

FIG. 7 is a table showing coefficients of determination and mean square errors of each of the nonlinear regression models calculated in step S230 of the method for predicting software failure time illustrated in FIG. 3.

FIG. 8 is a graph for explaining a change in the predicted failure time compared to the number of failures (1 to 30) by the method of predicting the software failure time shown in FIG. 3 by comparing each nonlinear regression model with an actual value.

9 is a table for explaining by comparing each nonlinear regression model with respect to basic statistical information on the number of failures (1 to 30) predicted by the method for predicting a software failure time shown in FIG. 3.

FIG. 10 is a graph for explaining a change in the predicted failure time compared to the number of failures 31 to 40 by the method of predicting the software failure time shown in FIG. 3 by comparing each of the nonlinear regression models.

11 is a table for explaining by comparing each of the nonlinear regression models with respect to basic statistical information about the number of failures 31 to 40 predicted by the method for predicting a software failure time illustrated in FIG. 3.

The organic operation of the apparatus for predicting failure time based on a nonlinear regression model according to another embodiment of the present invention will be described in detail with reference to FIGS. 1 to 11.

In the software failure time data collected by the trend test analysis unit 110, as shown in FIG. 3, a failure number and a failure time are mapped to each other.

In order for the trend test analysis unit 110 to verify the validity of the software failure time data shown in FIG. 4, a trend analysis must be preceded, and the present invention uses the Laplace trend test analysis shown in FIG. 5.

Here, the Laplace trend test analysis is a method for testing in which the homogeneous Poisson process is a null hypothesis, and the non-homogeneous Poisson process with a monotonic failure function as an alternative hypothesis.If the null hypothesis is true, the test statistic is asymptotically standard normal. It refers to the method of analyzing the trend test that becomes a distribution.

In general, in the case of the arithmetic mean increase pattern, the result of the arithmetic mean test indicates an increase in reliability, and the result of the Laplace trend analysis test in which the Laplace coefficient value varies between -2 and 2 indicates stable reliability.

As shown in Fig. 5, the result of the Laplace trend test is that the Laplace factor exists between -2 and 2, so there is no extreme value, so using this data to ensure reliability It can be seen that it is efficient to present a model.

The present invention uses a growth regression model, a quadratic regression model, and an S-curve regression model, which are nonlinear regression models to predict future software failure times.

Nonlinear regression model is a logarithmic or weighted nonlinear case (curved linear model), an explanatory variable for the number of failures (x _i ) and a dependent variable for failure time (y _i ). It can be converted into a linear model as shown in the following equation where the relationship is linear.

[Equation 1]

, 즉 평균이 0, 표준 편차가 σ인 정규 분포를 나타낸다.Here, b ₀ and b ₁ represent regression coefficients,

, That is, a normal distribution with a mean of 0 and a standard deviation of σ.

In addition, the present invention uses a growth regression model such as the following equation to predict a future software failure time.

[Equation 2]

,(

)

,(

)

Here, β ₀ and β ₁ are estimates of b ₀ and b ₁ , respectively, x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for failure time.

In addition, the present invention uses a quadratic regression model such as the following equation to predict a future software failure time.

[Equation 3]

Here, β _{0 ,} β ₁ and β ₂ are estimates of b _0, b ₁ and b _{2 ,} respectively, x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for failure time.

In addition, the present invention uses an S-curve regression model as shown in the following equation to predict future software failure time.

[Equation 4]

, (

)

, (

)

Here, β ₀ and β ₁ are estimates of b ₀ and b ₁ , respectively, x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for failure time.

,

,

)는 모두 계산되었으나, S-곡선 회귀 모형 및 성장 회귀 모형에 대하여 계산한 회귀 계수(b₂)의 모수 추정치(

)는 계산되지 않았다.As shown in FIG. 6, the parameter estimate of the regression coefficients (b ₁ , b ₂ , b ₃ ) calculated by the parameter estimate calculation unit 120 for the quadratic regression model, the S-curve regression model, and the growth regression model (

,

,

) Were all calculated, but the parameter estimate of the regression coefficient (b ₂ ) calculated for the S-curve regression model and the growth regression model (

) Was not calculated.

및 평균 제곱 오차(MSE)를 계산한다.On the other hand, the optimal model reference calculation unit 130 is a determination coefficient for determining an efficient failure time prediction model

And the mean squared error (MSE) is calculated.

및 평균제곱 오차(MSE)를 이용한 방법을 사용하며, 이러한 최적 모형을 결정하는 기준을 수정할 수 있다.That is, as a method of determining the criterion of a better prediction technique for measuring the error representing the predicted and actual values of the test model, the coefficient of determination

And a method using a mean squared error (MSE), and a criterion for determining such an optimal model can be modified.

는 회귀선에 의한 제곱의 합(SSR), 제곱 오차의 합(SSE) 및 총 제곱(SST)이라고 정의되며, 데이터의 변형을 설명하는데 적합도가 얼마나 성공적인지 측정할 수 있다. Coefficient of determination

Is defined as the sum of squares (SSR), sum of squared errors (SSE), and total squares (SST) by the regression line, and can measure how successful the fit is to explain the transformation of the data.

는 다음의 수학식과 같이 정의된다.Coefficient of determination

Is defined as the following equation.

[Equation 5]

,

,

,

는 y_i의 추정치이고,

는 y_i의 평균값이다.At this time,

,

,

,

Is the estimate of y _i ,

Is the average value of y _i .

The following is a criterion for determining an efficient model, and the mean squared error (MSE) is defined as the following equation.

[Equation 6]

은 시간

까지 나타난 에러들의 누적 함수를 의미하고,

는

시점까지 평균값 함수로부터 추정된 에러의 누적 개수를 의미한다. From here,

Silver time

It means the cumulative function of the errors shown up to,

Is

It means the cumulative number of errors estimated from the average value function up to the point in time.

Also, n is the number of observations, and k is the number of parameters.

Usually, the smaller the mean squared error is, the better, so it can be seen that the mean squared error model with the minimum value is more efficient.

Therefore, a relatively efficient model is obtained when the mean square error (MSE) value is small in comparison of simulation results.

및 평균 제곱 오차(MSE)를 각 비선형 회귀 모형 별로 비교하면, 성장 회귀 모형이 2차 회귀 모형 및 S-곡선 회귀 모형보다 결정 계수

가 높고, 평균 제곱 오차(MSE)가 작은 것으로 나타났다.As shown in FIG. 7, the determination coefficient calculated by the optimal model reference calculation unit 130

And mean squared error (MSE) for each nonlinear regression model, the growth regression model is more determined than the quadratic regression model and the S-curve regression model.

Was high and the mean square error (MSE) was small.

Accordingly, the optimal model determination unit 220 determines that the growth regression model is more effective in terms of suitability than the other nonlinear regression models.

As shown in Figure 8, using a growth regression model, a quadratic regression model, and an S-curve regression model, which are nonlinear regression models from time point-1 (number of failures) to time point -30 (number of failures), failures against actual values Shows the result of predicting time.

In Figure 8, all models are estimated to be similar to actual values, but in particular, the growth regression model shows relatively better predictive ability, and the S-curve regression model predicts the failure time lower than the actual value (underestimated). It was found that the second-order model predicted the failure time higher (overestimated).

As shown in FIG. 9, when comparing the basic statistical information predicted by the failure time prediction unit 210 for each nonlinear regression model, the estimated maximum and minimum values of the S-curve regression model range from 10.181 to 224.132. Since it is stable, it can be seen that the S-curve regression model shows better properties and range than the rest of the models.

In addition, since the quadratic model is the highest in standard deviation and variance and the S-curve regression model is relatively small, the average value is the highest in the quadratic model and the S-curve regression model is the lowest.

Therefore, in order to use a stable quadratic model, the optimum model determination unit 220 determines that a test for variance measurement must be preceded.

As shown in FIG. 10, using a growth regression model, a quadratic regression model, and an S-curve regression model, which are nonlinear regression models from time point-31 (number of failures) to time point -40 (number of failures), Shows the result of predicting the failure time.

In Figure 10, as the number of failures increases, the predicted value for failure has a relatively high tendency for the growth regression model to rise.In particular, it was confirmed that the S-curve regression model was relatively low when compared to the growth regression model and the quadratic regression model. .

This is because the S-curve regression model appears relatively low and the growth regression model is the highest for range estimation (especially, estimation of standard deviation and variance).

As shown in FIG. 11, if the failure time prediction unit 210 compares the basic statistical information predicted from the time point-31 (the number of failures) to the time point -40 (the number of failures) for each nonlinear regression model, the S-curve regression model The estimated range of is 5.282, which shows a significantly lower predicted result when compared with the growth regression model with an estimated value of 1185.198 and the quadratic regression model with an estimated value of 653.879.

Therefore, in order to use a stable growth regression model, the optimum model determination unit 220 determines that a test for variance measurement must be preceded.

Meanwhile, the recording medium according to the present invention is a computer-readable recording medium in which a program for executing the method for predicting a software failure time based on a nonlinear regression model according to the present invention described above is recorded in a computer.

In the recording medium according to an embodiment of the present invention, a trend detection unit predicts a software failure time using a nonlinear regression model; And determining, by a failure time analysis unit, an optimal parameter statistical model for the predicted software failure time using a determination coefficient and a mean square error. Is included.

The recording medium according to another embodiment of the present invention includes the steps of: (a) verifying the validity of the data with software failure time data collected by a trend test analysis unit; (b) receiving, by a parameter estimate calculation unit, the verified failure time data and calculating a parameter estimate for a nonlinear regression model; (c) calculating, by an optimal model reference calculation unit, a determination coefficient and a mean square error for determining a failure time prediction model; (d) predicting failure time data by analyzing a future failure time with respect to an actual value by receiving the calculated determination coefficient and the mean square error calculated by a failure time prediction unit; And (e) determining an optimal parameter statistical model by analyzing the predicted failure time data by an optimal model determination unit. Is included.

The computer-readable recording medium may include program instructions, data files, data structures, and the like alone or in combination.

The program instructions recorded on the recording medium may be specially designed and configured for the embodiment, or may be known and usable to those skilled in computer software.

Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. -A hardware device specially configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like.

Examples of the program instructions include not only machine language codes such as those produced by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like.

The hardware device described above may be configured to operate as one or more software modules to perform the operation of the embodiment, and vice versa.

As described above, the present invention is a nonlinear regression model capable of predicting a future failure time by examining the cutoff time and the prediction time using a nonlinear regression model with different error periods, and determining a model with a high coefficient of determination and a low mean square error. It provides a method of predicting the failure time of the based software and a computer-readable recording medium.

Through this, in the field of software system design and software reliability, software developers and operators can accurately predict and consider the increase in information needed to inspect data, enabling rapid and accurate analysis and prediction of software failure times, thereby improving software stability. Can be improved.

In the above, several preferred embodiments of the present invention have been described with some examples, but the description of the various various embodiments described in the "Specific Contents for Carrying out the Invention" section is merely exemplary, and the present invention is Those of ordinary skill in the art to which it belongs will be well understood from the above description that the present invention can be variously modified to be implemented or equivalent to the present invention.

In addition, since the present invention can be implemented in a variety of other forms, the present invention is not limited by the above description, and the above description is intended to complete the disclosure of the present invention, and is generally used in the technical field to which the present invention pertains. It should be understood that it is provided only to completely inform the scope of the present invention to those skilled in the art, and that the present invention is only defined by each claim of the claims.

100: trend test section
110: trend test analysis unit
120: parameter estimate calculation unit
130: optimal model reference calculation unit
200: failure time analysis unit
210: failure time prediction unit
220: optimal model decision section

Claims (12)

Predicting a software failure time by using a nonlinear regression model by a trend test unit; And
Determining, by a failure time analysis unit, an optimal parameter statistical model for the predicted software failure time using a determination coefficient and a mean square error;
Characterized in that it comprises a,
A method of predicting software failure time based on a nonlinear regression model.
(a) verifying the validity of the data using the software failure time data collected by the trend test analysis unit;
(b) receiving, by a parameter estimate calculation unit, the verified failure time data and calculating a parameter estimate for a nonlinear regression model;
(c) calculating, by an optimal model reference calculation unit, a determination coefficient and a mean square error for determining a failure time prediction model;
(d) predicting failure time data by analyzing a future failure time with respect to an actual value by receiving the calculated determination coefficient and the mean square error calculated by a failure time prediction unit; And
(e) determining an optimal parameter statistical model by analyzing the predicted failure time data by an optimal model determination unit;
Characterized in that it comprises a,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 2,
Step (a)
Characterized in that the validity of the data is verified using a Laplace trend test analysis technique,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 2,
Step (a)
The explanatory variable (x _i ) for the number of failures and the dependent variable (y _i ) for the failure time are transformed into a linear model by Equation 1, which is a linear relationship,
Equation 1 is

as,
B ₀ and b ₁ are regression coefficients,

, That is, characterized in that it is a normal distribution with a mean of 0 and a standard deviation of σ,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 4,
The nonlinear regression model is
It characterized in that any one of a growth regression model, a quadratic regression model, and an S-curve regression model,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 5,
The growth regression model is defined by Equation 2,
Equation 2 is

,(

)as,
Wherein the β ₀ and β ₁ are the estimates of the b ₀ and the b ₁ , respectively, the x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for the failure time,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 5,
The quadratic regression model is defined by Equation 3,
Equation 3 is

as,
The β _0, the β ₁ and the β ₂ are the estimated values of the b _0, the b ₁ and the regression coefficient b ₂ , respectively, the x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for the failure time. Characterized in that,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 5,
The S-curve regression model is defined by Equation 4,
Equation 4 is

, (

)as,
Wherein the β ₀ and β ₁ are the estimates of the b ₀ and the b ₁ , respectively, the x _i is an explanatory variable for the number of failures, and y _i is a dependent variable for the failure time,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 2,
In step (c),
The coefficient of determination is defined by Equation 5 as the sum of squares (SSR), the sum of squared errors (SSE), and the total squares (SST) by a regression line,
Equation 5 is

Is,
remind

, remind

, remind

Is, above

Is the estimate of y _i , where

Is the average value of y _i ,
A method of predicting software failure time based on a nonlinear regression model.
The method of claim 2,
In step (c),
The mean squared error is defined by Equation 6,
Equation 6 is

Is,
remind

Silver time

The cumulative function of the errors shown to, above

Is the cumulative number of errors estimated from the average value function up to the time point x _i , n is the observed value, and k is the number of parameters,
A method of predicting software failure time based on a nonlinear regression model.
Predicting a software failure time by using a nonlinear regression model by a trend test unit; And
Determining, by a failure time analysis unit, an optimal parameter statistical model for the predicted software failure time using a determination coefficient and a mean square error;
Characterized in that it comprises a,
Computer-readable recording medium of a method of predicting software failure time based on a nonlinear regression model.
(a) verifying the validity of the data using the software failure time data collected by the trend test analysis unit;
(b) receiving, by a parameter estimate calculation unit, the verified failure time data and calculating a parameter estimate for a nonlinear regression model;
(c) calculating, by an optimal model reference calculation unit, a determination coefficient and a mean square error for determining a failure time prediction model;
(d) predicting failure time data by analyzing a future failure time with respect to an actual value by receiving the calculated determination coefficient and the mean square error calculated by a failure time prediction unit; And
(e) determining an optimal parameter statistical model by analyzing the predicted failure time data by an optimal model determination unit;
Characterized in that it comprises a,
Computer-readable recording medium of a method of predicting software failure time based on a nonlinear regression model.

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