# Deep-Learning Software Reliability Model Using SRGM as Activation Function
## 1 Introduction  
Software is widely used in many fields. There is no place where it is not used from the smallest part to the entire part. Currently, the fields of artificial intelligence and big data have gained considerable attention and are based on software along with high-performance hardware. These fields require many calculations. Therefore, to make the calculations as simple as possible and to learn quickly, the code, structure, and configuration of the software are extremely important. As the artificial intelligence and big data industries develop, they must rely heavily on software. If part of the developed software fails owing to a code error or an error in the calculation process, it can cause many problems. The error in the computation may produce unexpected results, or the error may cause a malfunction in a machine that operates in real time; therefore, research to improve software reliability has been steadily conducted [1, 2, 3, 4]. There is plenty of study in the field of system reliability that extends beyond software reliability. The study is being conducted on how to ensure reliability and service in more complex systems than software. It has been shown that information about system failures and errors is important to increase the reliability of a system and to troubleshoot problems. In addition, sustainable development is becoming a very important topic in system reliability. Sustainable development means operating production processes and developing products in a way that is environmentally friendly and considers the environment andeconomic aspects of workers. To create a sustainable production environment, breakdowns and energy waste must be minimized or eliminated, and maintenance is essential. For sustainable development, technologies equipped with intelligent learning self-diagnosis and self-adaptive technologies that monitor, control, and process data are needed [5; 6]. Software reliability is a field in which how well software works is measured, and software reliability growth model (SRGM) is developed based on software failure. Because software failure data follows a Poisson distribution that indicates the number of failures that occurred during a period of time, the SRGM currently being studied is based on the SRGM that assumes a nonhomogeneous Poisson process (NHPP) [7]. The SRGM assuming NHPP, which started with [PERSON] [8], has been extended to SRGMs reflecting various assumptions such as independent assumptions, uncertain operating environments, and dependent assumptions. From a parametric perspective, SRGMs are developed by estimating optimal parameters. In addition, software reliability models from a non-parametric perspective that depend on data have been continuously studied, based on deep learning or other machine learning algorithms such as deep neural networks and recurrent neural networks [9; 10]. However, in deep learning, the typical nonlinear activation function used can cause training difficulties due to the saturation behavior, so new activation functions such as noisy or self-regularized non-monotonic activation function are being studied [11; 12]. In this study, based on the theoretical background of the problem of activation function, we would like to propose a deep learning software reliability model by combining a software reliability model from a parametric perspective and a software reliability model using deep learning from a non-parametric perspective. Because the structure of the existing software reliability model is similar to the sigmoid function, the proposed software reliability model utilizes the shape of the sigmoid function and applies it to learning instead of the activation function of deep learning. This is a deep learning software reliability model by using an activation function with mathematical assumptions to solve the problem of deep learning that only depends on data. The superiority of the model is demonstrated by comparing 10 criteria using two datasets.