In the software testing phase, software reliability growth models (SRGMs) are commonly used to evaluate the reliability of software systems. Traditional SRGMs are restricted by their assumption of a continuous growth pattern for the failure detection rate (FDR) throughout the testing phase. However, the assumption is compromised by Change-Point phenomena, where FDR fluctuations stem from variations in testing personnel or procedural modifications, leading to reduced prediction accuracy and compromised software reliability assessments. Therefore, the objective of this study is to improve software reliability prediction using a novel approach that combines genetic algorithm (GA) and deep learning-based SRGMs to account for the Change-point phenomenon. The proposed approach uses a GA to dynamically combine activation functions from various deep learning-based SRGMs into a new mutated SRGM called MuSRGM. The MuSRGM captures the advantages of both concave and S-shaped SRGMs and is better suited to capture the change-point phenomenon during testing and more accurately reflect actual testing situations. Additionally, failure data is treated as a time series and analyzed using a combination of Long Short-Term Memory (LSTM) and Attention mechanisms. To assess the performance of MuSRGM, we conducted experiments on three distinct failure datasets. The results indicate that MuSRGM outperformed the baseline method, exhibiting low prediction error (MSE) on all three datasets. Furthermore, MuSRGM demonstrated remarkable generalization ability on these datasets, remaining unaffected by uneven data distribution. Therefore, MuSRGM represents a highly promising advanced solution that can provide increased accuracy and applicability for software reliability assessment during the testing phase.

We discuss software reliability assessment considering multiple changes of software fault-detection phenomenon. The testing-time when the characteristic of the software failure-occurrence or fault-detection phenomenon changes notably in the testing-phase of a software development process is called change-point. It is known that the occurrence of the change-point influences the accuracy for the software reliability assessment based on a software reliability growth models, which are mainly divided into software failure-occurrence time and fault counting models. This paper discusses software reliability growth modeling frameworks considering with the effect of the multiple change-point occurrence on the software reliability growth process in software failure-occurrence time and fault counting modeling. And we show numerical illustrations for the software reliability analyses based on our models by using actual data.

Initial growth of GaP on Si substrates using metalorganic vapor phase epitaxy was studied. Si substrates were exposed to PH3 preflow for 15 s or 120 s at 830 after they were preheated at 925. Atomic force microscopy (AFM) revealed that the Si surface after preflow for 120 s was much rougher than that after preflow for 15 s. After 1.5 nm GaP deposition on the Si substrates at 830, GaP islands nucleated more uniformly on the Si substrate after preflow for 15 s than on the substrate after preflow for 120 s. After 3 nm GaP deposition, layer structures were observed on a fraction of Si surface after preflow for 15 s. Island-like structures remained on the Si surface after preflow for 120 s. After 6 nm GaP deposition, the continuity of GaP layers improved on both substrates. However, AFM shows pits that penetrated a Si substrate with preflow for 120 s. Transmission electron microscopy of a GaP layer on the Si substrate after preflow for 120 s revealed that V-shaped pits penetrated the Si substrate. The preflow for a long time roughened the Si surface, which facilitated the pit formation during GaP growth in addition to degrading the surface morphology of GaP at the initial growth stage. Even after 50 nm GaP deposition, pits with a density on the order of 107 cm-2 remained in the sample. A 50-nm-thick flat GaP surface without pits was achieved for the sample with PH3 preflow for 15 s. The PH3 short preflow is necessary to produce a flat GaP surface on a Si substrate.

A realistic computer graphics (CG) model of root growth that accounts for the effects of soil obstruction and moisture variations is proposed. While the exposed parts of plants have been modeled extensively in CG, realistic root models have received little attention, and the potential effects of root characteristics on the growth of foliage has yet to be considered in detail. The proposed model represents roots as series of bend points and link points and defines the root systems as a layered structure formed by roots connected via link points. This approach allows for two general types of root systems based on branching probabilities of lateral and adventitious roots: main root systems consisting of a thick main root and thinner lateral roots, and fibrous root systems consisting of adventitious roots of relatively uniform diameter. The model also expresses the behavior of root growth in terms of hydrotropism, gravitropism, flexion and growth inhibition by assigning gravity, moisture and consistency parameters to underground voxels. The model is shown through simulations of various growth conditions to generate individualized root systems that reflect the growth environment and characteristics of the plant.

In this paper, we propose a new software reliability growth model which is the mixture of two exponential reliability growth models, one of which has the reliability growth and the other one does not have the reliability growth after the software is released upon completion of testing phase. The mixture of two such models is characterized by a weighted factor p, which is the proportion of reliability growth part within the model. Firstly, this paper discusses an optimal software release problem with regard to the expected total software cost incurred during the warranty period under the proposed software reliability growth model, which generalizes Kimura, Toyota and Yamada's (1999) model with consideration of the weighted factor. The second main purpose of this paper is to apply the Bayesian approach to the optimal software release policy by assuming the prior distributions for the unknown parameters contained in the proposed software reliability growth model. Some numerical examples are presented for the purpose of comparing the optimal software release policies depending on the choice of parameters by the non-Bayesian and Bayesian methods.

I describe a software reliability growth model that yields accurate parameter estimates even with a small amount of input data. The model is based on a proposed discrete analog of a Gompertz equation that has an exact solution. The difference equation tends to a differential equation on which the Gompertz curve model is defined, when the time interval tends to zero. The exact solution also tends to the exact solution of the differential equation when the time interval tends to zero. The discrete model conserves the characteristics of the Gompertz model because the difference equation has an exact solution. Therefore, the proposed model provides accurate parameter estimates, making it possible to predict in the early test phase when software can be released.

Non-homogeneous Poisson Processes (NHPP's) can be applied for analyzing reliability growth models for hardware and/or software. Evaluating the Mean Time Between Failures (MTBF's) for such processes, we can evaluate the present status (the degree of improvement). However, it is difficult to evaluate the MTBF's for such processes analytically except the simplest cases. The so-called instantaneous MTBF's which can be easily evaluated are applied in practice instead of the exact MTBF's. In this paper, we discuss both MTBF's analytically, and derive the conditions for the existence of both exact and instantaneous MTBF's. We further illustrate both MTBF's for the Weibull process and S-shaped reliability growth model numerically.

In this paper, we propose a plausible software reliability growth model by applying a mathematical technique of stochastic differential equations. First, we extend a basic differential equation describing the average behavior of software fault-detection processes during the testing phase to a stochastic differential equation of ItÔ type, and derive a probability distribution of its solution processes. Second, we obtain several software reliability measures from the probability distribution. Finally, applying a method of maximum-likelihood we estimate unknown parameters in our model by using available data in the actual software testing procedures, and numerically show the stochastic behavior of the number of faults remaining in the software system. Further, the model is compared among the existing software reliability growth models in terms of goodness-of-fit.