A method, system and application for analyzing the impact of fault detection rate on software reliability

Abstract

The present invention belongs to the technical field of software fault data identification, and discloses a method, system, and application for analyzing the impact of fault detection rate on software reliability. The method for analyzing the impact of fault detection rate on software reliability includes the following steps: analyzing the form of fault detection rate b(t) of the same type, and for a single SRGM single FDS multiple FDR mode and a multiple SRGM multiple FDS multiple FDR mode, using information entropy combined with a TOPSIS decision algorithm to obtain a partial order sorting of the SRGM model corresponding to the software fault detection rate function; analyzing the performance impact factors of FDR on the SRGM model, selecting the SRGM with a fault detection rate to establish a distance in the actual software testing process, and realizing test resource allocation and optimal release time. The present invention has a strong guiding role in parameter model selection, determining the optimal release time, and the like in software reliability modeling.

Description

Technical Field

[0001] The present invention belongs to the technical field of software fault data identification, and in particular relates to a method, system and application for analyzing the impact of fault detection rate on software reliability. Background Art

[0002] With the development of information technology and the internet, computer applications are becoming increasingly widespread. As the primary vehicle for users to use computers and the provider of their functionality, computer software plays a vital role in production and daily life. To meet rising expectations for software functionality, software scale and complexity continue to increase. As software scale grows, maintaining software quality becomes a crucial component of software development and testing. Software reliability is a crucial factor in software quality; high-quality software is inherently reliable. The Software Reliability Growth Model (SRGM) is a key method for software reliability analysis and is currently the mainstream analysis method. In general, the SRGM model consists of two basic parameters: total software faults, which represents the overall number of faults in a software system; and fault detection rate, which describes the testing capability of a software testing environment. During software testing, testers continuously discover and fix faults. To better understand software reliability and achieve expected (release) requirements, it is necessary to analyze the role of FDR in reliability analysis.

[0003] The FDR characterizes the comprehensive capabilities of the test environment, testing technology, test resource consumption, and tester skills. Objectively, differences in test environments and tester implementation strategies result in different system engineering projects exhibiting distinct external characteristics during testing. From the perspective of mathematical modeling, the differences between different models are closely related to the FDR. Thus, the FDR characterizes the overall test effectiveness, making it a key evaluation factor influencing SRGM performance. It is of great significance for software reliability modeling, software fault prediction, optimal release timing, and testing cost control.

[0004] Through the above analysis, the problems and defects of the existing technology are as follows:

[0005] (1) The existing technology has low accuracy in predicting the number of software failures and high control testing costs.

[0006] (2) The existing technology does not select an appropriate fault detection rate during the actual software testing process, resulting in uneven distribution of test resources and low release time accuracy, which limits its practical application. Summary of the Invention

[0007] To overcome the problems existing in the related art, the disclosed embodiment of the present invention provides a method for analyzing the impact of fault detection rate on software reliability.

[0008] The technical solution is as follows: a method for analyzing the impact of fault detection rate on software reliability, applied to an information data processing terminal, the method for analyzing the impact of fault detection rate on software reliability comprising the following steps:

[0009] S1, analyze the form of fault detection rate b(t) of the same type, including multiple expressions of common constant type, FDR, S type, and exponential type;

[0010] S2, for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode, the information entropy is combined with the TOPSIS decision algorithm to obtain the partial order ranking of the SRGM model corresponding to the software fault detection rate function;

[0011] S3, analyzes the factors affecting the performance of the SRGM model by FDR, and selects the SRGM with fault detection rate to establish distance in the actual software testing process to achieve test resource allocation and optimal release time.

[0012] In one embodiment, in step S1, analyzing the fault detection rate b(t) of the same type includes the following steps:

[0013] (1) Software failure meets the NHPP process;

[0014] (2) The number of faults detected within (t + Δt) is proportional to the number of faults remaining in the current software;

[0015] (3) The software repair process suffers from incomplete debugging and the introduction of new faults;

[0016] (4) According to steps (1)-(3), the SRGM model corresponding to different fault detection rates is solved. The differential equation of the SRGM model is:

[0017]

[0018] Where m(t) is the fault detection function, which represents the number of faults detected during software testing; b(t) is the fault detection rate function, with a value between (0, 1); a(t) represents the total number of software faults, which is set as a constant or a function of the test time t; p is the fault repair probability, with a value between (0, 1). Different forms of functions are substituted into the SRGM model differential equation to solve the fault detection function.

[0019] In step S1, analyzing the fault detection rate b(t) of the same type further includes:

[0020] Step 1: Selecting a set of SRGMs on a predetermined FDS, wherein the set of SRGMs includes the software reliability growth model established from the perspective of FDR;

[0021] Step 2: Establish a set of FDRs to be observed and select them by collecting the FDRs that appear more frequently in the current analysis;

[0022] Step 3: Establish a set of observation points for evaluating FDR and its possible impact on SRGM.

[0023] In one embodiment, in step S2, the single SRGM single FDS multiple FDR mode includes: substituting multiple b(t) functions into m(t) under a determined SRGM by changing the FDR therein to observe the SRGM performance at this time;

[0024] Different FDRs are introduced into SRGM, and the fitting and prediction values ​​obtained by observation are used to give the FDR partial order ranking results through the EvaluateFDREffectOnSRGM-SSSFMF decision algorithm;

[0025] The EvaluateFDREffectOnSRGM_SSSFMF decision algorithm includes:

[0026] Input: SRGM model m(t) selected (through a large number of experiments) and failure data set DS, fault detection rate vector FDRSet = [bt1, bt2, ..., bt m ], fitting and prediction weight vector W;

[0027] Output: FDR partial order set FDRSet;

[0028] (1)For each b(t)in(FDRSet){

[0029] MT[i]=Fitting(m(t),DS,b(t))

[0030] MSE[i]=CalculateMSE(MT[i])

[0031] R_square[i]=CalculateR_square(MT[i])

[0032] Variation[i]=CalculateVariation(MT[i])

[0033] RE[i]=CalculateRE(MT[i])}

[0034] (2) FDRSet = SortFDR(MT, MSE, R_square, Variation, RE, W) / / Get the FDR partial order set after processing by the decision algorithm;

[0035] (3)Return FDRSet;

[0036] The selection of model fitting indicators in SSSFMF is mainly analyzed from two aspects: fitting and prediction. The fitting indicators selected are mean square error (MSE), coefficient of determination (R 2 ) and variance; the prediction index RE is comprehensively analyzed by observing the shape of the prediction curve and the average of the absolute values ​​of the last five values ​​of the RE curve. The subjective observation results are quantified with the help of the hierarchical analysis process (AHP) and finally converted into quantitative performance indicators.

[0037] In one embodiment, in step S2, the multi-SRGM multi-FDS multi-FDR mode includes:

[0038] 1) When faced with multiple fixed SRGM conditions and multiple FDS, multiple b(t) functions are substituted into m(t) in groups to observe the SRGM performance at this time;

[0039] 2) The selected multiple SRGMs and multiple FDSs are divided into several groups. Different FDRs are introduced into the SRGMs in each group. By obtaining the comprehensive fitting and prediction values, the comprehensive performance value of the FDR is obtained.

[0040] 3) Perform steps 1) to 2) above for each group to obtain the comprehensive performance values ​​of multiple groups with different FDRs;

[0041] 4) Finally, the ranking results of all FDRs are given by the EvaluateFDREffectOnSRGM-MSMFMF decision algorithm;

[0042] The EvaluateFDREffectOnSRGM_MSMFMF decision algorithm includes:

[0043] Input: (Through a large number of experiments) the selected SRGM model set SRGMSet and the failure data set DSSet, the fault detection rate vector FDRSet = [bt1, bt2, ..., bt m ], fitting and prediction weight vector W;

[0044] Output: FDR partial order set FDRSet;

[0045] Step 1,

[0046] For each b(t)in(FDRSet){

[0047] For each m(t)in(SRGMSet){

[0048] MT[j]=Fitting(m(t),DSSet[j],b(t))

[0049] MSE[j]=CalculateMSE(MT[j])

[0050] R_square[j]=CalculateR_square(MT[j])

[0051] Variation[j]=CalculateVariation(MT[j])

[0052] RE[j]=CalculateRE(MT[j])

[0053] FDRSingleValue[j]=GetFDR(MT[j],MSE[j],R_square[j],Variation[j],RE[j],W)} / / Get the FDR single performance value for each different SRGM in each group;

[0054] FDRIntegratedValue[i]=GetFullFDR(FDRSingleValue)} / / Get the FDR comprehensive performance value of each group;

[0055] Step 2, FDRSet = SortFDR(FDRIntegratedValue) / / obtain the FDR partial order set processed by the decision algorithm;

[0056] Step 3, Return FDRSet.

[0057] In one embodiment, SortFDR() in step (2) implements the sorting of SRGM models. The basic sorting algorithm adopts the SRGM decision algorithm based on TOPSIS, including the following steps: the SRGM decision algorithm based on TOPSIS uses information entropy + TOPSIS to sort the selected models, and obtains the SRGM with comprehensive performance, so as to analyze the impact of fault detection rate on software reliability.

[0058] In one embodiment, the ranking of the selected models using information entropy + TOPSIS includes:

[0059] (i) The k fitting and prediction values ​​of n SRGMs on a specified data set are arranged and combined into a multi-attribute decision matrix MADM (Mutltiple Attribute Decision Matrix) as shown in formula (2);

[0060]

[0061] (ii) Calculating weights based on information entropy

[0062] Regularize each column of MADM to get formula (3)

[0063]

[0064] in

[0065] (iii) Then calculate the information entropy of each indicator based on the regularization matrix, as shown in formula (4):

[0066]

[0067] Among them E i is the information entropy of the i-th indicator, E0 is the information entropy constant, and its value is (lnk) -1 ;

[0068] Calculate the divergence of each indicator to get

[0069] D i =1-E i (5)

[0070] Calculate the information entropy weight of each indicator

[0071]

[0072] (iv) Decision-making method based on TOPSIS

[0073] Based on the decision matrix DM, select the maximum value r of each column (n)· With the minimum value r (1)· The positive optimal solution and negative worst solution of SRGM are formed, and the optimal and worst decision matrix PNDM (Positive Negative Decision Matrix) is as follows:

[0074]

[0075] In order to eliminate the influence of the dimensions of different index values, the matrix is ​​standardized as follows

[0076]

[0077] where r ij represents the element in row i and column j in PNDM, and S j It represents the mean and standard deviation of each performance index of SRGM, and the calculation formula is:

[0078] The matrix after normalization is as follows

[0079]

[0080] Then multiply each column by the weight corresponding to each performance indicator to obtain the weighted optimal and worst decision matrix WPNDM, as shown in formula (10):

[0081]

[0082] (v) Calculate the performance index of each model (p i1 ,p i2 ,…,p ik ) to the forward optimal solution set (p (n)1 , p (n)2 ,…,p (n)k ) and the negative worst solution set (p (1)1 ,p (1)2 ,…,p (1)k ) and then calculate the closeness H i , determine the final SRGMs partial order;

[0083] The i-th model SRGM i Distance to the forward optimal solution The calculation method is shown in formula (11):

[0084]

[0085] The i-th model SRGM i Distance to the worst negative point The calculation method is shown in formula (12):

[0086]

[0087] Then the i-th model SRGM i The degree of closeness to the ideal solution H i It can be calculated by formula (13)

[0088]

[0089] The closeness H of n SRGMs i Sort and get the partial order set [H (1) ,H (2) ,...,H (n) ], where H (n) The corresponding SRGM is the best model for this data set, H (1)The corresponding model is the worst performing model under this data set;

[0090] In step S3, based on the ranking results of all FDRs, the effects of different FDR functions on the performance of SRGM are analyzed.

[0091] Another object of the present invention is to provide a system for analyzing the impact of fault detection rate on software reliability, which implements the method for analyzing the impact of fault detection rate on software reliability, and is applied to an information data processing terminal. The system for analyzing the impact of fault detection rate on software reliability comprises:

[0092] The fault detection rate expression acquisition module is used to analyze the fault detection rate b(t) forms of the same type, including multiple expressions of common constant type, FDR type, S type, and exponential type;

[0093] The SRGM model partial ordering acquisition module is used to obtain the partial ordering of the SRGM model corresponding to the software fault detection rate function by combining information entropy with the TOPSIS decision algorithm for single SRGM single FDS multiple FDR mode and multiple SRGM multiple FDS multiple FDR mode;

[0094] The software performance influencing factor analysis module is used to analyze the performance influencing factors of FDR on the SRGM model, select the SRGM with fault detection rate to establish distance in the actual software testing process, and realize test resource allocation and optimal release time.

[0095] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the method for analyzing the impact of fault detection rate on software reliability.

[0096] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the method for analyzing the impact of fault detection rate on software reliability.

[0097] Another object of the present invention is to provide an information data processing terminal, which, when executed on an electronic device, provides a user input interface to implement the method for analyzing the impact of fault detection rate on software reliability.

[0098] Combining all the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0099] First, in view of the technical problems existing in the above-mentioned prior art and the difficulty of solving these problems, this paper closely combines the technical solutions to be protected by the present invention and the results and data during the research and development process, and analyzes in detail and in depth how the technical solutions of the present invention solve the technical problems and some creative technical effects brought about by solving the problems. The specific description is as follows:

[0100] Fault detection rate is one of the main parameters of software reliability model, and different forms of fault detection rate have different efficacy effects. The present invention analyzes the impact of fault detection rate on software reliability, and proposes two empirical analysis schemes based on information entropy and superiority-inferiority distance decision algorithm: single reliability model single failure data set multiple fault detection rate and multiple reliability growth model multiple failure data set multiple fault detection rate, aiming to comprehensively analyze the efficacy impact of fault detection rate. After experimental analysis, for a single reliability model single data set, the impact of fault detection rate on software reliability is mainly related to the failure data set, and the performance differences of different fault detection rates under different data sets are large. On multiple software reliability models and multiple data sets, the software reliability model corresponding to the power function and S-type fault detection rate has better comprehensive performance, and the software reliability model corresponding to the exponential fault detection rate has poorer comprehensive performance. The present invention has a strong guiding role in parameter model selection, determining the optimal release time, etc. in software reliability modeling.

[0101] Second, considering the technical solution as a whole or from the perspective of the product, the technical effects and advantages of the technical solution to be protected by the present invention are described in detail as follows:

[0102] The present invention mainly analyzes the impact of different FDR models on the performance of the SRGM model and conducts an empirical analysis. First, the forms of different types of fault detection rates b(t) are analyzed. There are a total of four types and six expressions: constant type, power function type, S type, and exponential type. Subsequently, for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode, the information entropy is combined with the TOPSIS decision algorithm to obtain the partial order sorting of the SRGM model corresponding to the software fault detection rate function, and the performance influencing factors of FDR on the SRGM model are analyzed. Through experiments, it is found that the power function FDR performs well in convex growth data sets, and the exponential type performs better in S-type growth and concave growth data sets. The present invention has certain guiding significance for selecting a suitable fault detection rate to establish a distance SRGM in the actual software testing process, and provides a reference for test resource allocation and optimal release. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0104] Figure 1 This is a flow chart of a method for analyzing the impact of fault detection rate on software reliability provided by an embodiment of the present invention;

[0105] Figure 2 is a b(t) evaluation and decision flow chart of Solution 1 provided in an embodiment of the present invention;

[0106] Figure 3 This is a b(t) evaluation and decision flow chart for Solution 2 provided in an embodiment of the present invention;

[0107] Figure 4 2. Schematic diagram of a system for analyzing the impact of fault detection rate on software reliability provided by an embodiment of the present invention;

[0108] Figure 1: Fault detection rate expression acquisition module, used to analyze the same type of fault detection rate b(t) form, including multiple expressions of common constant type, FDR type, S type, and exponential type;

[0109] The SRGM model partial ordering acquisition module is used to obtain the partial ordering of the SRGM model corresponding to the software fault detection rate function by combining information entropy with the TOPSIS decision algorithm for single SRGM single FDS multiple FDR mode and multiple SRGM multiple FDS multiple FDR mode;

[0110] Software performance influencing factors analysis module DETAILED DESCRIPTION

[0111] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0112] 1. Explanation of the embodiment:

[0113] Starting from the fault detection rate, this paper establishes a unified model to address the shortcomings of current analysis. It proposes two evaluation mechanisms: the "single SRGM single FDS multiple FDR mode" and the "multiple SRGM multiple FDS multiple FDR mode" as well as a corresponding evaluation algorithm based on multi-attribute decision-making. It analyzes the relationship between the reliability model, FDS and FDR, and based on the experimental results of FDR on the reliability model and FDS, applies multi-attribute decision-making for comprehensive evaluation. The evaluation is implemented in combination with different practical scenarios to analyze the impact of the fault detection rate on the effectiveness of the SRGM.

[0114] like Figure 1 As shown, an embodiment of the present invention provides a method for analyzing the impact of fault detection rate on software reliability, which is applied to an information data processing terminal. The method for analyzing the impact of fault detection rate on software reliability includes the following steps:

[0115] S101, analyzing the form of the fault detection rate b(t) of the same type, including multiple expressions of common constant type, FDR type, S type, and exponential type;

[0116] S102, for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode, using information entropy combined with the TOPSIS decision algorithm, derive the partial order ranking of the SRGM models corresponding to the software fault detection rate function;

[0117] S103, analyzing the factors affecting the performance of the SRGM model by FDR, and selecting the SRGM that establishes the distance by fault detection rate in the actual software testing process to achieve test resource allocation and optimal release time.

[0118] Example 1

[0119] To facilitate understanding of the technical innovation of the present invention, further explanation will be given below in conjunction with a review of the fault detection rate of the prior art.

[0120] The fault detection rate (fDR) represents the average probability of detecting a single fault per unit time at the current moment, or the fault detection rate, and is typically denoted by b(t). The concept of b(t) = b, a constant, indicates that the fault detection rate remains constant throughout the software testing process. This is the earliest proposed form of the fault detection rate. While not entirely consistent with the actual software testing process, it does represent the basic trends of the software reliability growth model and offers some guiding significance. b(t) is a function that varies with the test time t. This account for factors such as tester proficiency, test costs, and code complexity that change over time during the software testing process. Compared to a constant, a variable b(t) offers greater flexibility, leading to more accurate testing models.

[0121] In the previous analysis, the basic types and forms of fault detection rates have been summarized. There are four types and six function forms, as shown in Table 1.

[0122] Table 1 Fault detection rate type

[0123]

[0124] The following is an analysis of the above six types of fault detection rates, and the present invention analyzes the impact of fault detection rate on SRGM.

[0125] 1. Modeling the impact of fault detection rate on reliability model

[0126] 1.1 Basic Framework

[0127] First, the present invention provides the common assumptions established by SRGM:

[0128] (1) Software failure meets the NHPP process;

[0129] (2) The number of faults detected within (t + Δt) is proportional to the number of faults remaining in the current software;

[0130] (3) There are incomplete debugging and new faults introduced during the software repair process.

[0131] Based on the above assumptions, the present invention solves the SRGM model corresponding to different fault detection rates. The basic differential equation form is:

[0132]

[0133] Where m(t) is the fault detection function, representing the number of faults detected during software testing. b(t) is the fault detection rate function, with a value between (0, 1). a(t) represents the total number of software faults and can be set as a constant or a function of the test time t. p is the fault repair probability, with a value between (0, 1). Substituting different forms of functions into the differential equation can solve the fault detection function.

[0134] The present invention will proceed from the following three steps to gradually determine FDR, SRGM and FDS.

[0135] Step 1: Based on the previous analysis results and a large number of experiments of the present invention, a set of SRGMs with excellent performance on the predetermined FDS is selected. These SRGM sets include the reliability models established from the FDR perspective obtained above.

[0136] Step 2: Establish the FDR set to be observed. Although this set cannot be obtained from the previous experiments, it can be selected by collecting the FDRs that appear more frequently in the current analysis.

[0137] Step 3: Establish a set of observation points for evaluating FDR and its possible impact on SRGM.

[0138] After determining the relevant model, an empirical analysis is conducted based on two schemes to comprehensively explore the impact of fault detection rate on SRGM performance.

[0139] Solution 1: Single SRGM, single FDS, multiple FDRs

[0140] Under a certain SRGM (i.e., m(t)) condition, the FDR can be changed by substituting multiple b(t) functions into m(t) to observe the SRGM performance at this time. This situation is called the single SRGM single FDS multiple FDR mode.

[0141] At this time, for the selected SRGM and FDS, since the former has a good fitting and prediction ability for the latter, different FDRs are brought into the SRGM for experiments under this good situation. The fitting and prediction values ​​obtained through observation and the appropriate decision algorithm can give the FDR ranking result (i.e., partial order set). Figure 2 Table 2 and Table 3 respectively describe the basic process of this solution 1 and the corresponding execution algorithm EvaluateFDREffectOnSRGM-SSSFMF.

[0142] Table 2 Scheme 1 execution algorithm EvaluateFDREffectOnSRGM-SSSFMF

[0143]

[0144]

[0145] The selection of model fitting indicators in SSSFMF is mainly analyzed from two aspects: fitting and prediction. The fitting indicators selected are mean square error (MSE), coefficient of determination (R 2 ) and variance (Variation). Their representative meanings and calculation formulas are shown in Table 3. The prediction index RE is primarily based on a comprehensive analysis of the shape of the prediction curve and the average of the absolute values ​​of the last five values ​​of the RE curve. The subjective observations are quantified using the Analytic Hierarchy Process (AHP) and ultimately converted into a quantitative performance indicator. The quantitative values ​​of the RE index are shown in Table 4 and are divided into five levels. The final RE index is the standardized quantitative value.

[0146] Table 3 Fitting index

[0147]

[0148] Table 4 Quantitative levels of RE indicators

[0149] describe Worst Difference generally good most Quantized value 1 3 5 7 9

[0150] The SortFDR() function is used to sort the models. The basic sorting algorithm is the SRGM decision algorithm based on TOPSIS. Please refer to 1.2 for details.

[0151] In this single-SRGM single-FDS multiple FDR mode, since the analysis is based on a single SRGM and failure data set FDS, it is limited to a specific software testing environment. Based on the analysis results, it is easy to improve the test strategy so that its fault detection rate can be improved in the direction of meeting the test requirements.

[0152] Solution 2: Multiple SRGM, multiple FDS, and multiple FDR modes

[0153] When faced with multiple certain SRGM (i.e., m(t)) conditions and multiple FDSs, multiple b(t) functions can be grouped and introduced into m(t) to observe the SRGM performance at this time. This situation is called the multi-SRGM multi-FDS multi-FDR mode.

[0154] Based on Scheme 1, the selected SRGMs and FDSs are divided into several groups. Within each group, different FDRs are introduced into the SRGMs for experimentation. By observing the combined fit and prediction values, a comprehensive performance value for this FDR is obtained. This experiment is repeated for each group, resulting in comprehensive performance values ​​for multiple groups with different FDRs. Finally, a suitable decision algorithm is used to determine the ranking of all FDRs (i.e., a partially ordered set). Figure 2 (b(t) evaluation and decision process of Scheme 2) and Table 5 respectively describe the basic process of Scheme 2 and the corresponding execution algorithm EvaluateFDREffectOnSRGM—MSMFMF.

[0155] Table 5 Scheme 2 execution algorithm EvaluateFDREffectOnSRGM-MSMFMF

[0156]

[0157] In this multi-SRGM, multi-FDS, and multi-FDR model, since the analysis is based on multiple SRGMs and multiple failure datasets (FDS), it is not limited to a specific software testing environment. This allows for comprehensive analysis of the actual performance of different FDRs and common situations in the software testing process, thereby obtaining valuable conclusions for software testing development and guiding practice.

[0158] 1.2 SRGM decision algorithm based on TOPSIS

[0159] The SRGM model ranking problem involves ranking models based on their fit and prediction results for real failure datasets. It is a multi-criteria decision-making problem. The weights of each criterion are calculated using information entropy. The specific decision-making algorithm is the TOPSIS algorithm, based on the distance between superior and inferior solutions. Using information entropy combined with TOPSIS, the selected models are ranked to identify the SRGM with the best overall performance. This allows analysis of the impact of fault detection rate on software reliability.

[0160] The k fitting and prediction values ​​of n SRGMs on a specified data set are arranged and combined into a multi-attribute decision matrix MADM (Mutltiple Attribute Decision Matrix) as shown in formula (2).

[0161]

[0162] 1.2.1 Calculating weights based on information entropy

[0163] Regularize each column of MADM to get formula (3)

[0164]

[0165] in,

[0166] Then calculate the information entropy of each indicator based on the regularization matrix, as shown in formula (4)

[0167]

[0168] Among them E i is the information entropy of the i-th indicator, E0 is the information entropy constant, and its value is (lnk) -1 .

[0169] Calculating the divergence of each indicator can be obtained

[0170] D i =1-E i (5)

[0171] Calculate the information entropy weight of each indicator

[0172]

[0173] 1.2.2 Decision-making method based on TOPSIS

[0174] Based on the decision matrix DM, select the maximum value r of each column (n)· With the minimum value r (1)·The positive optimal solution and negative worst solution of SRGM are formed, and the optimal and worst decision matrix PNDM (Positive Negative Decision Matrix) is as follows:

[0175]

[0176] In order to eliminate the influence of the dimensions of different index values, the matrix is ​​standardized as follows

[0177]

[0178] where r ij represents the element in row i and column j in PNDM, and S j It represents the mean and standard deviation of each performance index of SRGM, and the calculation formula is:

[0179] The matrix after normalization is as follows

[0180]

[0181] Then multiply each column by the weight corresponding to each performance indicator calculated in Section 1.2.1 to obtain the weighted optimal and worst decision matrix WPNDM (Weighted Positive Negative Decision Matrix), as shown in Equation (10):

[0182]

[0183] Then we need to calculate the performance indicators of each model (p i1 ,p i2 ,…,p ik ) to the forward optimal solution set (p (n)1 ,p (n)2 ,…,p (n)k ) and the negative worst solution set (p (1)1 ,p (1)2 ,…,p (1)k ) and then calculate the closeness H i , determine the final SRGMs partial order.

[0184] The i-th model SRGM i Distance to the forward optimal solution The calculation method is shown in formula (11):

[0185]

[0186] The i-th model SRGM iDistance to the worst negative point The calculation method is shown in formula (12)

[0187]

[0188] Then the i-th model SRGM i The degree of closeness to the ideal solution H i It can be calculated by formula (13)

[0189]

[0190] The closeness H of n SRGMs i Sorting can get the partial order set of SRGM under this data set [H (1) ,H (2) ,...,H (n) ], where H (n) The corresponding SRGM is the best model for this data set, H (1) The corresponding model is the worst model under this dataset. Based on the ranking results of all FDRs, the effects of different FDR functions on the performance of SRGM are analyzed.

[0191] Example 2

[0192] An embodiment of the present invention provides a system for analyzing the impact of fault detection rate on software reliability, which implements the method for analyzing the impact of fault detection rate on software reliability. The system is applied to an information data processing terminal. The system includes:

[0193] Fault detection rate expression acquisition module 1 is used to analyze the form of fault detection rate b(t) of the same type, including multiple expressions of common constant type, FDR type, S type, and exponential type;

[0194] SRGM model partial ordering acquisition module 2 is used to obtain the partial ordering of the SRGM model corresponding to the software fault detection rate function by using information entropy combined with the TOPSIS decision algorithm for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode;

[0195] The software performance influencing factor analysis module 3 is used to analyze the performance influencing factors of FDR on the SRGM model, select the SRGM with fault detection rate to establish distance in the actual software testing process, and realize the test resource allocation and optimal release time.

[0196] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0197] Since the information interaction, execution process, etc. between the above-mentioned devices / units are based on the same concept as the method embodiment of the present invention, their specific functions and technical effects can be found in the method embodiment part and will not be repeated here.

[0198] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of the present invention. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0199] 2. Application Examples

[0200] Application Example 1

[0201] An embodiment of the present invention also provides a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, wherein the processor implements the steps of any of the above-mentioned method embodiments when executing the computer program.

[0202] Application Example 2

[0203] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments can be implemented.

[0204] Application Example 3

[0205] An embodiment of the present invention also provides an information data processing terminal, which is used to provide a user input interface to implement the steps in the above-mentioned method embodiments when executed on an electronic device. The information data processing terminal is not limited to mobile phones, computers, and switches.

[0206] Application Example 4

[0207] An embodiment of the present invention further provides a server, which is used to provide a user input interface to implement the steps in the above method embodiments when executed on an electronic device.

[0208] Application Example 5

[0209] An embodiment of the present invention provides a computer program product. When the computer program product is run on an electronic device, the electronic device can implement the steps of the above-mentioned method embodiments when executing the computer program product.

[0210] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process of the above-mentioned embodiment method by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file, or some intermediate form. The computer-readable medium can at least include: any entity or device capable of carrying computer program code to the camera / terminal device, recording medium, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium. For example, a USB flash drive, mobile hard drive, magnetic disk, or optical disk.

[0211] III. Evidence of the relevant effects of the embodiments:

[0212] 1 Experimental Setup

[0213] For Solution 1: Single SRGM Single FDS Multiple FDR Mode, to reduce complexity, a perfect debugging model is used here, where it is assumed that the total number of software faults is a fixed constant, that is, a(t) = a, and the fault repair probability is fixed to 1, that is, p = 1. The model expression is shown in Table 6.

[0214] Table 6 Models involved in the comparison of Scheme 1

[0215]

[0216] The above is the SRGM model corresponding to different b(t) functions under the perfect assumption. Then, fitting and prediction are performed on a real failure dataset of a database application software released by IBM to observe the impact of different FDRs on the SRGM model.

[0217] For Option 2 (Multi-SRGM, Multi-FDS, Multi-FDR), a software reliability growth model was selected. Two SRGM models were chosen: perfect fault recovery and imperfect fault recovery. The basic assumptions for perfect fault recovery are the same as those for Option 1. For the imperfect fault recovery SRGM model, we selected the software total fault model a(t), which performed well in the previous analysis. For ease of calculation, we assumed the fault repair probability p(t) = p. The model expressions are shown in Table 7.

[0218] Table 7 Models involved in the comparison of Scheme 2

[0219]

[0220] The above is the corresponding expression of m(t) for b(t) under the assumptions of imperfect and perfect error correction. Subsequently, fitting and prediction will be performed on three public real failure data sets. The growth curves of these three data sets are convex exponential growth (DS1), S-shaped growth (DS2), and concave exponential growth (DS3). This will analyze the comprehensive impact of FDR on SRGM performance for different SRGM models and different data sets.

[0221] 2 Experiment and analysis

[0222] 2.1 Experimental analysis of Scheme 1

[0223] This paper mainly analyzes the partial ordering of the single SRGM single FDS multiple FDR model based on the TOPSIS decision algorithm in the real failure data set. Based on parameter estimation, fitting performance calculation and prediction performance calculation, the initial multi-attribute decision matrix MADM1 of scheme 1 and the corresponding weights of each performance index are shown in Table 8 below. It can be seen that on the corresponding data set, the information entropy weight of the prediction performance index RE is the largest, the information entropy weight of the three fitting indicators MSE is the largest, and R 2 The weights are approximately the same as those of the Variation. The sum of all fitting index weights is 0.571, slightly larger than the weight of the prediction performance index.

[0224] Table 8 Performance indicators and corresponding weights

[0225]

[0226]

[0227] Calculations show how close the models (M-1 to M-6) in Scheme 1 are to the ideal solution, as shown in Table 9. It can be seen that in the perfect debugging test environment, for the selected data set, the M-2 model corresponding to the power function b2(t) performs best, the M-3 model corresponding to the S-type b3(t) and the M-6 model corresponding to the exponential type b6(t) perform well, and the M-1 model corresponding to the constant type b1(t) performs the worst.

[0228] Table 9: Model approximation of Scheme 1

[0229] Model Proximity H Sort order M-0 0.224379533 6 M-1 0.727315762 1 M-2 0.521737437 3 M-3 0.457707361 4 M-4 0.392164833 5 M-5 0.59279538 2

[0230] 2.2 Experimental analysis of Scheme 2

[0231] To further analyze the real-world performance of different FDRs, we selected three real-world failure data sets, DS1, DS2, and DS3, with different growth shapes: DS1 exhibits convex exponential growth, DS2 exhibits S-shaped growth, and DS3 exhibits concave exponential growth. The models (M-1 to M-12) in Table 5 were analyzed for fitting and prediction performance on these three data sets. Table 10 describes the performance indicators of the model in Scheme 2 after fitting and prediction on these three data sets, along with the weights calculated using information entropy.

[0232] Table 10 Performance indicators and weights of Scheme 2 model

[0233]

[0234]

[0235] In DS1, the prediction performance index RE has the largest weight, and the fitting performance index (MSE, R 2 The weights of the performance indicators (and Variation) are approximately the same, totaling 0.432171183. In DS2, the prediction performance indicator RE has the largest weight, while the MSE has a larger weight among the fitting performance indicators, with the total fitting performance weight being 0.31088595. In DS3, the MSE has the largest weight, with the total fitting performance weight being 0.785884519. The significant differences in the weights of performance indicators across different datasets indicate that their size is primarily determined by uncertainty. Greater uncertainty leads to greater confusion among the performance indicators of different models, and consequently, greater information entropy.

[0236] For the convex exponential growth failure data set DS1, the approximation values ​​of most SRGM models are greater than 0.5, indicating that the SRGM model has good fitting and prediction capabilities on the convex exponential growth data set. Among them, the M-7 model based on the imperfect error elimination assumption has the best performance, followed by the M-10 model; the M-5 and M-6 models based on the perfect error elimination assumption have the worst performance.

[0237] For the S-type growth failure dataset DS2, the overall closeness index value is slightly lower than that of DS1, indicating that the SRGM model has a slightly weaker fitting and prediction ability for the S-type growth dataset. Among them, the M-12 model based on the imperfect error elimination assumption has the best performance, followed by the M-9 model; the M-4 and M-5 models based on the perfect error elimination assumption have the worst performance.

[0238] For the concave exponential growth failure dataset DS3, the overall closeness index of each model is low, indicating that the SRGM model has the worst applicability for concave datasets. Among them, the M-5 model based on perfect error elimination has the best performance, followed by the M-1 model. The M-4 model based on the perfect error elimination assumption and the M-12 model based on the imperfect error elimination assumption have the worst performance.

[0239] For the two assumptions of the SRGM model: perfect fault elimination and imperfect fault elimination, according to the table above, the ranking performance of the models based on the imperfect fault elimination assumption (M-7 to M-12) is generally better than that of the models based on the perfect fault elimination assumption (M-1 to M-6). This shows that the model that takes into account the imperfect fault elimination assumption is more consistent with actual software testing work, and therefore has stronger universal applicability and more stable and excellent performance on different real failure data sets.

[0240] To further analyze the impact of different fault detection rate functions on SRGM, we performed a weighted average of the ranking sequences of the models on the three datasets to determine the weighted average order of the models. We categorized the growth of the collected datasets and found that 55% of the datasets exhibited a convex growth pattern consistent with DS1; 40% exhibited an S-shaped growth pattern consistent with DS2; and 5% exhibited a concave growth pattern. Therefore, we set the weight vector w to [0.55, 0.4, 0.05]. The results of the weighted calculation of the partial order are shown in Table 11.

[0241] Table 11 Model closeness of Scheme 2

[0242]

[0243] As can be seen from Table 11, except for the fault detection rate in the form of power function, which is ranked better than the imperfect fault detection rate under the perfect fault detection assumption, the performance of most models based on the imperfect fault detection assumption is better than that under the perfect assumption. This shows that the model considering the imperfect fault detection assumption is more in line with actual software testing work, and therefore has stronger universal applicability and more stable and excellent performance on different real failure data sets.

[0244] Table 12 Weighted sorting sequence of dataset

[0245] Model Weighted ranking value relative order M-0 6.05 7 M-1 4 2 M-2 5.25 6 M-3 10.9 11 M-4 10.5 10 M-5 10.7 12 M-6 5 3 M-7 4.6 4 M-8 4.35 5 M-9 4.2 1 M-10 6.15 8 M-11 5.9 9

[0246] Table 13 SRGM weighted sorting sequence

[0247] FDR Type Weighted sorting based on different SRGMs order constant 5.315 3 Power function 4.42 1 S-type 1 4.62 2 S-type 2 6.21 4 Complexity Index 1 7.455 5 Complexity Index 2 7.34 6

[0248] Finally, we weighted the SRGMs based on different assumptions to explore the impact of different fault detection rates on software reliability. Considering the model based on the imperfect fault detection assumption to be more relevant, we set its weight to 0.7, and the model based on the perfect fault detection assumption to 0.3. The resulting ranking weights and order are shown in Table 12. The power function and the first S-type FDR ranked first in overall performance, performing best across different datasets and SRGM assumptions. The two complex exponential FDRs had the worst overall performance. The power function FDR describes the gradual increase in fault detection rate with software runtime in software testing, meaning that the probability of detecting each fault gradually increases, which is consistent with real-world software testing environments. The S-type FDR is more flexible and adapts to complex testing environments, and its corresponding SRGM model also achieved good performance. The complex exponential FDR exhibited a decreasing trend with test time, initially increasing and then decreasing, which is significantly different from real-world testing environments, resulting in the worst SRGM performance.

[0249] 2. Experimental Results

[0250] The final ranking values ​​for Scheme 1 and Scheme 2 are not exactly the same, indicating that while our analysis is comprehensive, the selection of an FDR function for a specific dataset still involves some uncertainty. This requires comprehensive consideration of historical fault data, tester proficiency, program scale, and other factors before selecting one or more suitable FDR forms. Furthermore, analyzing the impact of fault detection rate on SRGM performance on a single dataset has some limitations, ultimately leading to different partial ranking results for the b(t) function for the two schemes.

[0251] According to the real failure data set and SRGM model selected by the present invention, the performance of the six FDR functions can be ranked as follows: b2(t)>b3(t)>b1(t)>b4(t)>b5(t)>b6(t). Sorting by the type of b(t) is as follows: power function>S-type>constant type>complex exponential type.

[0252] The performance of the SRGM corresponding to b(t) is related to the properties of the real failure dataset. The SRGM model corresponding to the power function FDR (Failure Detection Rate) that increases over time performs well on datasets with convex exponential growth. The complex exponential b6(t) is more suitable for datasets with complex S-shaped growth, and the exponential b5(t) performs better on datasets with concave growth. Furthermore, the S-shaped FDR performs very stably across a wide range of datasets in the present invention, demonstrating its high flexibility and wide adaptability.

[0253] The above description is only a preferred specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for analyzing the impact of fault detection rate on software reliability, characterized in that: Applied to an information data processing terminal, the method for analyzing the impact of fault detection rate on software reliability includes the following steps: S1, analyze the form of fault detection rate b(t) of the same type, including multiple expressions of common constant type, FDR type, S type, and exponential type; S2, for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode, the information entropy is combined with the TOPSIS decision algorithm to obtain the partial order ranking of the SRGM model corresponding to the software fault detection rate function; S3, analyze the factors affecting the performance of the SRGM model by the FDR type expression, select the fault detection rate in the actual software testing process to establish the distance SRGM model, and realize the test resource allocation and release time; In S2, the single SRGM single FDS multiple FDR mode includes: under a determined SRGM model, by changing the FDR therein, substituting multiple b(t) functions into m(t) to observe the performance of the SRGM model at this time; Different FDRs are introduced into the SRGM model, and the fitting and prediction values ​​obtained by observation are used to give the FDR partial order ranking results through the EvaluateFDREffectOnSRGM-SSSFMF decision algorithm; The EvaluateFDREffectOnSRGM_SSSFMF decision algorithm includes: Input: the selected SRGM model m(t) and failure data set DS, fault detection rate vector FDRSet = [bt1, bt2, ..., bt m ], fitting and prediction weight vector W; Output: FDR partial order set FDRSet; In S2, the multi-SRGM multi-FDS multi-FDR mode includes: 1) When faced with multiple fixed SRGM conditions and multiple FDS, multiple b(t) functions are substituted into m(t) in groups to observe the SRGM performance at this time; 2) The selected multiple SRGMs and multiple FDSs are divided into several groups. Different FDRs are introduced into the SRGMs in each group. By obtaining the comprehensive fitting and prediction values, the comprehensive performance value of the FDR is obtained. 3) Perform steps 1) to 2) above for each group to obtain the comprehensive performance values ​​of multiple groups with different FDRs; 4) Finally, the ranking results of all FDRs are given by the EvaluateFDREffectOnSRGM-MSMFMF decision algorithm; The EvaluateFDREffectOnSRGM_MSMFMF decision algorithm includes: Input: the selected SRGM model set SRGMSet and failure data set DSSet, fault detection rate vector FDRSet = [bt1, bt2, ..., bt m ], fitting and prediction weight vector W; Output: FDR partial order set FDRSet; In the FDR partial order sorting result given by the EvaluateFDREffectOnSRGM—SSSFMF decision algorithm in the single SRGM single FDS multi-FDR mode, and in the sorting result of all FDRs given by the EvaluateFDREffectOnSRGM—MSMFMF decision algorithm in step 4) of the multi-SRGM multi-FDS multi-FDR mode, the EvaluateFDREffectOnSRGM—SSSFMF decision algorithm and the EvaluateFDREffectOnSRGM—MSMFMF decision algorithm both adopt the SRGM decision algorithm based on TOPSIS. The SRGM decision algorithm based on TOPSIS adopts information entropy combined with TOPSIS to sort the selected SRGM model, and obtains the SRGM with comprehensive performance, so as to analyze the impact of fault detection rate on software reliability.

2. The method for analyzing the impact of fault detection rate on software reliability according to claim 1, characterized in that: In S1, the form of the fault detection rate b(t) of the same type is analyzed, which specifically includes the following steps: (1) Software failure meets the NHPP process; (2) The number of faults detected within time t+Δt is proportional to the number of faults remaining in the current software; (3) The software repair process suffers from incomplete debugging and the introduction of new faults; (4) Solve the SRGM model corresponding to different fault detection rates. The differential equation form of the SRGM model is: Where m(t) is the fault detection function, which represents the number of faults detected in software testing; b(t) is the fault detection rate function, with a value between (0, 1); a(t) represents the total number of software faults, which is set as a constant or a function of the test time t; p is the fault repair probability, with a value between (0, 1). Different forms of functions are substituted into the SRGM model differential equation to solve the fault detection function.

3. The method for analyzing the impact of fault detection rate on software reliability according to claim 1, characterized in that: The method of using information entropy combined with TOPSIS to sort the selected SRGM models includes: (i) The k fitting and prediction values ​​of n SRGMs on a specified data set are arranged and combined into a multi-attribute decision matrix MADM as shown in Equation (2); (ii) Calculating weights based on information entropy Regularize each column of MADM to get formula (3) in, (iii) Then calculate the information entropy of each indicator based on the regularization matrix, as shown in formula (4): Among them E i is the information entropy of the i-th indicator, E0 is the information entropy constant, and its value is (ln k) -1 ; Calculate the divergence of each indicator to get D i =1-E i (5) Calculate the information entropy weight of each indicator (iv) Decision-making method based on TOPSIS Based on the decision matrix DM, select the maximum value r of each column (n)· With the minimum value r (1)· The positive optimal solution and negative worst solution of SRGM are formed, and the optimal and worst decision matrix PNDM is obtained as follows: In order to eliminate the influence of the dimensions of different index values, the matrix is ​​standardized as follows where r ij represents the element in row i and column j in PNDM, and S j It represents the mean and standard deviation of each performance index of SRGM, and the calculation formula is: The matrix after normalization is as follows Then multiply each column by the weight corresponding to each performance indicator to obtain the weighted optimal and worst decision matrix WPNDM, as shown in formula (10): (v) Calculate the performance index of each model (p i1 ,p i2 ,…,p ik ) to the forward optimal solution set (p (n)1 ,p (n)2 ,…,p (n)k ) and the negative worst solution set (p (1)1 ,p (1)2 ,…,p (1)k ) and then calculate the closeness H i , determine the final SRGMs partial order; The i-th model SRGM i Distance to the forward optimal solution The calculation method is shown in formula (11): The i-th model SRGM i Distance to the worst negative point The calculation method is shown in formula (12): Then the i-th model SRGM i The degree of closeness to the ideal solution H i Calculated by formula (13) The closeness H of n SRGMs i Sort and get the partial order set [H (1) ,H (2) ,...,H (n) ], where H (n) The corresponding SRGM is the best model for this data set, H (1) The corresponding model is the worst performing model under this data set; In step S3, based on the ranking results of all FDRs, the effects of different FDR functions on the performance of SRGM are analyzed.

4. A system for analyzing the impact of fault detection rate on software reliability, which implements the method for analyzing the impact of fault detection rate on software reliability as described in any one of claims 1 to 3, characterized in that: Applied to an information data processing terminal, the system for analyzing the impact of fault detection rate on software reliability includes: The fault detection rate expression form acquisition module (1) is used to analyze the form of the fault detection rate b(t) of the same type, including multiple expressions of common constant type, FDR type, S type, and exponential type; The SRGM model partial ordering acquisition module (2) is used to obtain the partial ordering of the SRGM model corresponding to the software fault detection rate function by using information entropy combined with the TOPSIS decision algorithm for the single SRGM single FDS multiple FDR mode and the multiple SRGM multiple FDS multiple FDR mode; The software performance influencing factor analysis module (3) is used to analyze the performance influencing factors of FDR on the SRGM model, select the SRGM with fault detection rate to establish distance in the actual software testing process, and realize test resource allocation and optimal release time.

5. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the method for analyzing the impact of fault detection rate on software reliability as described in any one of claims 1 to 3.

6. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the method for analyzing the impact of fault detection rate on software reliability according to any one of claims 1 to 3.

7. An information data processing terminal, characterized in that: When the information data processing terminal is implemented on an electronic device, it provides a user input interface to implement the method for analyzing the impact of fault detection rate on software reliability as described in any one of claims 1 to 3.

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