CN112612719B - Weighted standardized optimization selection software reliability model method - Google Patents
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Abstract
The invention belongs to the technical field of software models, and particularly relates to a weighted standardized optimization selection software reliability model method. The proposed method of weighted normalization can be divided into three steps. The first step calculates a model evaluation value for each software reliability model, which can be represented by a matrix. Then, a normalization process, i.e., a normalization calculation of the attribute values of the software reliability model, is performed. And secondly, determining the importance degree and influence of each attribute value of the software reliability model on the performance of the evaluation model, namely, the weight value of the attribute of the software reliability model. And thirdly, sorting according to the standardized attribute value and the weight value of each model, and selecting an optimal software reliability model. The method for optimally selecting the software reliability model can select the optimal software reliability model and can be effectively applied to actual software tests.
Description
Technical Field
The invention belongs to the technical field of software models, and particularly relates to a weighted standardized optimization selection software reliability model method.
Background
In recent years, with the development of information technology, the reliability of software systems in computers has become a focus of attention. To evaluate reliability problems of software systems, researchers have built a variety of software reliability models. Because of the complexity of software system development, testing and debugging, no software reliability model has been available to date for reliability evaluation of all software systems. The corresponding reliability evaluation can only be performed for a specific software system. How to determine which software reliability model to use in which case to evaluate the reliability of the software is a tricky problem. In view of this real problem, researchers have proposed selecting the best software reliability model under the current software testing environment by optimizing the reliability model selection method. And it is used to evaluate the reliability of the software system.
Generally, there are two methods for optimizing and selecting a software reliability model, one is a single-attribute optimization and selection method. The method uses only one evaluation standard of the software reliability model as a single attribute of the model, compares the single attributes of a plurality of software reliability models, and finally selects the optimal software reliability model. For example, KHOSHGOFTAAR and WOODCOCK propose to use the evaluation criterion "Akaike Information Criterion (AIC)" of the software reliability model as a single attribute for selecting the software reliability model, and to use the single attribute AIC value for selecting the optimal software reliability model. Another method of optimally selecting a software reliability model is a multi-attribute optimization selection method. The method takes a plurality of software reliability model evaluation standards as the multi-attribute of the model, and finally selects the optimal software reliability model through the comprehensive comparison of the multi-attribute values. For example, shalma et al propose to compare with a plurality of software reliability model criteria, i.e., the multi-attribute of the model, calculate the error Distance (DBA) of the model multi-attribute, and finally find the optimal software reliability model.
Because the comparison of the software reliability models is a comparison of comprehensive performance, the selection of the optimal software reliability model by a single attribute method may not necessarily reflect the performance of the actual software reliability model. Compared with a single-attribute method, the multi-attribute method can evaluate the comprehensive performance of the software reliability model from multiple aspects. However, since the evaluation criteria of a model in multiple attributes may be negative, bias may be negative, for example. Its negative value merely indicates that the difference between the total estimated value and the total actual value is negative, i.e. the total estimated value is smaller than the total actual value. And comparison with the negative value of this attribute has no practical meaning. Therefore, how to effectively use the evaluation criteria of the model in multiple attributes is a problem to be solved urgently.
Disclosure of Invention
The invention provides a method for weighting, standardizing, optimizing and selecting a software reliability model. The method mainly considers the situation that the evaluation standard of the software reliability model, namely the attribute of the model, is negative, because the comprehensive attribute comparison of the model by using the method has no practical meaning. And secondly, considering influence and importance of the attribute of each model in optimizing and selecting the model, namely the weight. Through the research on the two points, we propose a method for optimizing and selecting a model based on weighted normalization. Experimental results show that the method for optimally selecting the software reliability model can select the optimal software reliability model and can be effectively applied to actual software tests.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the invention provides a method for weighting, standardizing, optimizing and selecting a software reliability model, which comprises the following steps:
step 1, fitting and estimating parameter values of the software reliability model by using a fault data set, and then calculating attribute values of the software reliability model by using an evaluation standard of the software reliability model, which can be expressed as,
wherein y is μν A v attribute value representing a μ software reliability model;
step 2, carrying out standardization processing on the attribute values of the model, namely taking absolute values of the attribute values of the model, and then calculating the attribute standardization values of the model;
step 3, calculating the weight of the software reliability model attribute;
and 4, calculating the sequencing value of each software reliability model.
Further, the calculation of the attribute standardization value of the model in the step 2 includes two cases:
(1) The smaller the attribute value of the software reliability model, the better the performance of the model, its normalization can be expressed as,
(2) The greater the attribute value of the software reliability model, the better the performance of the model, its normalization can be expressed as,
wherein i represents a software reliability model, j represents an attribute of the software reliability model, |y ij | max Representing the maximum value in the j-th attribute in the i-th software reliability model.
To remove noise disturbances present in the attribute values of each software reliability model, and to facilitate comparison of model attribute values. We normalize the attribute values of the model. Since the attribute values of the model may be negative, negative values are not significant at normalization. Furthermore, a negative value of the attribute value of the model only indicates that the software reliability model estimates a smaller number of faults than actually observed. We can take absolute values of the model's attribute values and then calculate the model's attribute normalization values.
Further, the calculation of the attribute weight of the software reliability model in the step 3 includes two cases:
(1) The smaller the attribute value of the software reliability model, the better the performance of the model, its weight can be expressed as,
(2) The greater the attribute value of the software reliability model, the better the performance of the model, its weight can be expressed as,
wherein i represents a software reliability model, j represents an attribute of the software reliability model, |y ij | max Represents the maximum value, |y, in the j-th attribute in the i-th software reliability model ij | min Representing the minimum value in the j-th attribute in the i-th software reliability model.
Further, the calculation formula of the ranking value of the software reliability model in the step 4 is as follows:
substitution of formulas (1-4) into formula (5) can be expressed as,
from the values of equation (5) and equation (6), a ranking value for each software reliability model is calculated. The smaller its value indicates the better the software reliability model performance. That is, by selecting the model with the smallest ranking value as the optimal software reliability model.
Still further, the software reliability models in step 1 include a Goel-Okumto model, a Delayed S-shaped model, an information S-shaped model, a general purpose Goel model, a Modified Duane model, a logistic Growth model, a Musa-Okumoto model, a Yamada Imperfect debugging model 1,Yamada Imperfect debugging model 2, a Kapur 1 model, a P-N-Z model, a P-Z model, and a Zhang-Teng-Pham model.
Criteria for evaluating the software reliability model include Bias, MSE, MAE, MEOP, PRR, variance, RMSPE, R 2 SSE and TS.
Compared with the prior art, the invention has the following advantages:
for the case that a negative value exists in the evaluation standard of the current model, and the case cannot be effectively used as the performance standard for evaluating the current software reliability model, an optimization selection method of a software reliability model with simple weighted standardization is provided. The collected software fault data sets were tested with two actual software, and corresponding experiments were performed with 13 multiple software reliability models and 10 evaluation criteria for the software reliability models. Experimental results indicate that the proposed method can effectively select the optimal software reliability model suitable for the current software testing environment. The developer and manager can use the method to select the optimal software reliability model to predict the residual faults in the software and evaluate the reliability degree of the software. The method for optimally selecting the software reliability model is simple and effective, and can select the optimal software reliability model and play an important role in the actual software testing process. The method can lay a foundation for future researchers to further study on the basis of the method for optimizing and selecting the software reliability model.
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FIG. 1 is a comparison of the number of faults detected by accumulation of models using the fault dataset-1.
FIG. 2 is a comparison of the number of faults detected by the accumulation of models using the fault dataset-2.
Detailed Description
The following describes the technical scheme in the embodiment of the present invention in detail with reference to the embodiment of the present invention and the accompanying drawings. It should be noted that variations and modifications can be made by those skilled in the art without departing from the principles of the present invention, which are also considered to be within the scope of the present invention.
Example 1
Selection of software reliability models
To verify the effectiveness of the proposed optimization method, a correlation experiment was performed with 13 traditional classical software reliability models.
The 13 traditional classical software reliability models include the Goel-Okumto (G-O) model, the Delayed S-shaped (DSS) model, the information S-shaped (ISS) model, the Generalized Goel (GGO) model, the Modified Duane (MD) model, the Logical Growth (LG) model, the Musa-Okumoto (MO) model, the Yamada Imperfect debugging model 1 (YIDM 1), the Yamada Imperfect debugging model 2 (YIDM 2), the Kapur 1 model, the P-N-Z model, the P-Z model and the Zhang-Teng-Pham model. Wherein the perfect debug model includes 7, a Goel-Okumto (G-O) model, a Delayed S-shaped (DSS) model, an information S-shaped (ISS) model, a Generalized Goel (GGO) model, a Modified Duane (MD) model, a Logical Growth (LG) model and a Musa-Okumoto (MO) model. The imperfect debug models include 6, yamada Imperfect debugging model 1 (YIDM 1), yamada Imperfect debugging model 2 (YIDM 2), P-N-Z model, P-Z model, kapur 1 model and Zhang-Teng-Pham model. Among these models, there are curves for cumulatively detecting the number of faults as an S-type, for example, a Delayed S-shaped (DSS) model and an information S-shaped (ISS) model; there are also cumulative fault number curves that are concave, such as the Goel-Okumoto (G-O) model.
In general, the software reliability model selected is a representative model, including a substantially equal number of perfect and imperfect debug models selected. Although the software testing environment is complex, the software reliability model selected above can be adapted to most software testing environments. Through the optimization selection of the software reliability model, the software reliability model which is most suitable for the current software testing environment can be found. Table 1 details the case of the software reliability model selected above.
Table 1 software reliability model description selected
Example 2
Software reliability model evaluation criterion
To quantify the evaluation performance of the software reliability model, 10 evaluation criteria for the software reliability model are given herein. The 10 software reliability model evaluation criteria evaluate the performance of the software reliability model from different aspects. Note that 10 software reliability model evaluation criteria are referred to herein as 10 attributes of the software reliability model. The evaluation criteria of the 10 software reliability models include Bias, MSE, MAE, MEOP, PRR, variance, RMSPE, R 2 SSE and TS. The smaller the values of Bias, MSE, MAE, MEOP, PRR, variance, RMSPE, SSE and TS, among others, represent the better the performance of the software reliability model. R is R 2 The larger the value of (c) is, the better the fitting performance of the software reliability model is. Table 2 gives a detailed description of the 10 software reliability model evaluation criteria.
Table 2 software reliability model evaluation criteria description
Example 3
Selecting an optimal software reliability model
In general, in the case of large samples, the maximum likelihood estimation method is better than the least squares method. But in the case of small samples, the least squares method is better than the maximum likelihood estimation method. Since the fault dataset collected by the software test is a small sample, and the parameter values of the model estimated by the maximum likelihood estimation method have no maximum likelihood function values in some cases. Thus, to facilitate comparison and selection of models, a least squares method is employed herein to estimate parameter values for a software reliability model.
(1) Software failure data set
To verify the effectiveness of the proposed method, we performed corresponding experiments with two actual software test-collected fault datasets. The first software fault data set is detected and collected in the software project TROPICO-R. The software testing process comprises unit testing, integration testing, verification testing and actual operation testing. The collection of software fault data comes from four processes of software testing. The test time for which the fault dataset was collected was one time unit per ten days. A total of 461 faults were detected cumulatively over 81 time units. The second set of fault data is collected and consolidated by Musa. The faults in the second fault dataset are detected in the actual software project test system code SS 2. It takes 655 days to cumulatively detect 192 faults.
(2) Selecting an optimal software reliability model
Experiment one: we split the first failure data set into two parts. The first part is to fit and estimate the parameter values of the software reliability model with 70% of the fault data set, while the remaining part (30% of the fault data set) is used for the predicted performance comparison of the software reliability model. The calculation results are shown in Table 3.
TABLE 3 parameter values and attribute values for software reliability model (failure dataset-1)
From Table 3 we can see that the properties Bias, PRR and R2 have negative values. Their negative value means that the number of faults estimated by the software reliability model is smaller than the number of faults actually detected. Or underestimating the actual number of faults in the software. If the addition is simply performed at the time of normalization, the effect of the attribute of the model as an evaluation criterion cannot be effectively reflected.
Therefore, the absolute value method is adopted to ensure that the evaluation standard of the model plays an important role in the selection of the software reliability model. The calculation results are shown in Table 4.
Table 4 Attribute value weighted normalization result for software reliability model (failure dataset-1)
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After weighted normalization, it can be seen from Table 4 that the Goel-Okumoto model has better fitting and predictive performance than the other models. The method can be better suitable for the current software testing environment. It is used to predict and evaluate the reliability of software more accurately and reliably. Furthermore, from tables 3 and 4, it can be seen that not all values of the properties of the Goel-Okumoto model are smaller than the other models. For example, the PRR values of both the information S-shaped model and the Generalized Goel model are less than the PRR values of the Goel-Okumoto model. This means that it is difficult to determine which model is the optimal model from the property values of several models alone. The attribute values of the model need to be comprehensively considered to have practical significance. Table 5 is the software reliability model ordering result.
Table 5 software reliability model ordering results (failure dataset-1)
As can be seen from Table 5, the ordering of the Goel-Okumoto model is the first name. The second name is Kapur 1 model. The last name is Yamada Imperfect debugging model 1. The penultimate name is the Zhang-Teng-Pham model. This illustrates that the Goel-Okumoto model is better suited to the software testing environment in which the first failure data set is detected. The Goel-Okumoto model is used for predicting and evaluating the residual fault quantity and the reliability degree of the current software to be more practical. The Goel-Okumoto model is the best software reliability model currently selected, as compared to other models. This result can also be seen intuitively in fig. 1. In FIG. 1, the Goel-Okumoto model fits and predicts best, followed by the Kapur 1 model. Worst is Yamada Imperfect debugging model 1.
Experiment II: to further verify the effectiveness of the proposed optimization selection method, I performed a corresponding experiment with the failure dataset collected in another actual software test. 80% of the second fault data set is used as a parameter value estimate for the software reliability model, and the remaining 20% of the fault data set is compared to the predicted performance of the software reliability model. The calculation results of the parameter values and the attribute values of the software reliability model are shown in table 6.
TABLE 6 parameter values and attribute values for software reliability model (failure dataset-2)
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In table 6, both the properties Bias and PRR have negative values. Such negative values are detrimental to direct comparison of attribute values. And each attribute value of Yamada Imperfect debugging model 2 is substantially smaller than the attribute values of the other models. In order to effectively compare attribute values, we propose a method of weighted normalization after absolute values of attribute values to perform corresponding processing. The calculation results are shown in Table 7.
Table 7 Attribute value weighted normalization results for software reliability models (failure dataset-2)
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In table 7, it can be seen that the respective attribute values of the Yamada Imperfect debugging model 2 model are the smallest. After the weighted normalization synthesis process, the comparison of the software reliability models becomes straightforward and simple. Furthermore, it should be noted that although the Generalized gold model ranks last, there is also a minimum in its properties. For example, PRR is 0, indicating that its PRR value is the smallest of the current individual software reliability models. From another aspect, it is also explained that evaluating the performance of a software reliability model with a certain model evaluation criterion (attribute) does not fully reflect whether the software reliability model is suitable for the current software testing environment. Multiple attribute values need to be considered in combination to be able to select a model that is suitable for the current software testing environment. Table 8 is the software reliability model ordering result.
Table 8 software reliability model ordering results (failure dataset-2)
From table 8, it can be seen that Yamada Imperfect debugging model 2 is the best software reliability model selected, which ranks first. Yamada Imperfect debugging model 2 is more suitable for the current software testing environment, and can be used for predicting the number of faults remaining in the software and evaluating the reliability. The second rank is the P-N-Z model. The penultimate name is the Generalized gold model. The penultimate name is the Zhang-Teng-Pham model. From fig. 2, it can be seen that the best fitting and predicting performance is model Yamada Imperfect debugging 2. The fitted and predicted performance of the Generalized Goel model and the Zhang-Teng-Pham model are equivalent, and are the last models.
Claims (3)
1. A method for weighted normalization optimization selection of a software reliability model, comprising the steps of:
step 1, fitting and estimating parameter values of the software reliability model by using a fault data set, then calculating attribute values of the software reliability model by using an evaluation standard of the software reliability model, which are expressed as,
wherein y is μν A v attribute value representing a μ software reliability model;
step 2, carrying out standardization processing on the attribute values of the model, namely taking absolute values of the attribute values of the model, and then calculating the attribute standardization values of the model;
step 3, calculating the weight of the software reliability model attribute;
step 4, calculating the sequencing value of each software reliability model;
the calculation of the attribute standardization value of the model in the step 2 includes two cases:
(1) The smaller the attribute value of the software reliability model, the better the performance of the model, its normalization is expressed as,
(2) The greater the attribute value of the software reliability model, the better the performance of the model, its normalization is expressed as,
wherein i represents a software reliability model, j represents an attribute of the software reliability model, |y ij | max Representing the maximum value in the j-th attribute in the i-th software reliability model;
the calculation of the software reliability model attribute weight in the step 3 includes two cases:
(1) The smaller the attribute value of the software reliability model, the better the performance of the model, its weight is expressed as,
(2) The greater the attribute value of the software reliability model, the better the performance of the model, its weight expressed as,
wherein i represents a software reliability model, j represents an attribute of the software reliability model, |y ij | max Represents the maximum value, |y, in the j-th attribute in the i-th software reliability model ij | min Representing the minimum value in the j-th attribute in the i-th software reliability model;
the calculation formula of the sequencing value of the software reliability model in the step 4 is as follows:
wherein i represents a software reliability model, j represents an attribute of the software reliability model, |y ij | max Representing the maximum value in the j-th attribute in the i-th software reliability model.
2. The method for weighted normalization optimization of a software reliability model according to claim 1, wherein: the software reliability models in the step 1 comprise a Goel-Okumto model, a Delayed S-shaped model, an information S-shaped model, a general Goel model, a Modified Duane model, a logistic Growth model, a Musa-Okumoto model, a Yamada Imperfect debugging model 1,Yamada Imperfect debugging model 2, a Kapur 1 model, a P-N-Z model, a P-Z model and a Zhang-Teng-Pham model.
3. A method of weighted normalization optimization selection of a software reliability model according to claim 2, wherein: criteria for evaluating software reliability models include Bias, MSE, MAE, MEOP, PRR, variance, RMSPE, R 2 SSE and TS.
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