Jianfeng Yang

With the widespread application of Cyber-Physical Systems (CPS) in fields such as intelligent manufacturing and autonomous driving, their reliability has emerged as a critical challenge affecting overall system performance and safety. In response to the limitations of existing CPS reliability modeling approaches—such as insufficient structural expressiveness, difficulty in modeling heterogeneous software and hardware components, and the lack of a general modeling framework suitable for various system structures and component types—this paper proposes a universal CPS reliability modeling and fitting method based on survival signature theory. This method enables the separation of structural characteristics and component lifetime distributions without losing CPS structural information, thus providing a unified modeling framework for reliability evaluation under different distributional assumptions. Specifically, a generalized CPS reliability model is first developed using survival signature theory, incorporating structural assumptions, parameter configurations, and detailed mathematical derivations. The model's applicability is validated through systematic reliability calculations within a standard CPS framework. To better reflect real-world engineering scenarios, a CPS architecture with complex topological features is designed. Reliability variations in cyber and physical networks are then simulated using two distinct approaches: (1) an event-driven Monte Carlo method utilizing component reliability profiles for cyber network failure simulation, and (2) a time-censored Monte Carlo approach incorporating order statistics principles for physical network failure modeling. Building upon the simulation data, the paper innovatively introduces a reliability fitting method that combines survival signature and maximum likelihood estimation (MLE). In this approach, MLE is first applied to estimate the parameters of component lifetime distributions, after which the fitted CPS reliability is computed using the survival signature model. Finally, the proposed method is compared with five traditional regression models to assess its adaptability and performance across various network structures and simulation environments.

In this paper, the cyber physical system is divided into a software system and a hardware system, and both the software system and the hardware system each contain several subsystems. To solve the difficult problem of parameter estimation in parametric reliability models such as the non-homogeneous Poisson process under masked data, this paper proposed an additive reliability model of cyber physical systems based on local polynomial regression under masked data. This model uses the multinomial distribution to allocate the masked data and employs the local weighted least squares method to solve the reliability model. Finally, by using a set of open-source software failure data and a set of simulation data in the cyber physical system, this paper conducts a performance comparison and analysis between the proposed non-parametric reliability model and traditional reliability models. The empirical results show that the proposed reliability model performs better in terms of the fitting effect and demonstrates stronger applicability and superiority.

Cyber‐Physical Systems (CPS) are at the forefront of the intersection between information technology and physical operations, revolutionizing industries such as communication, automation, control, and intelligent transportation. However, evaluating the reliability of CPS, especially in the presence of multilateral random attacks, poses a complex challenge. This paper introduces an inventive probabilistic modeling approach to enhance the analysis of CPS reliability under the influence of multilateral random attacks. We provide an overview of fundamental CPS concepts and their significant role in modern society, followed by a comprehensive exploration of multilateral random attacks. Our novel probabilistic modeling approach is presented as a means to improve the accuracy and robustness of CPS reliability assessments when faced with multilateral random attacks. Numerical experiments and simulations validate the effectiveness of our innovative approach, emphasizing its potential to fortify the reliability of Cyber‐Physical Systems.

Within the software industry, the pace of software upgrades remains swift due to fierce market competition and rapidly evolving requirements. The fluctuating composition of development teams poses challenges in testing upgraded software. Despite this, limited attention has been devoted to testing strategies and reliability estimation for upgraded software systems, leveraging past testing data. Therefore, it is important and necessary to develop an effective testing strategy in order to ensure the product quality. In this paper, an upgradation software testing strategy adapted to requirements change will be proposed combined with the software development process of Parking Lot Mobile Payment System (PLMPS). In this approach, the testing information of the pre-versions and software functional structure will be fully used in upgradation software testing. Moreover, an upgradation software reliability model can be constructed based on proposed testing strategy. The proposed reliability model also can be applied to multi upgradation software systems. Furthermore, the proposed approach can help managers and developers generate testing cases and predict software reliability. A numerical example based on simulation data is given to illustrate its application in the modeling process.

In reality, sudden updates of software, attacks of hackers, influence of the Internet market, etc. can cause a surge in the number of open-source software (OSS) faults (this moment is the time when impulse occurs), which results in impulsive phenomenon. For the existing software reliability models, dynamic process of software fault is considered to be continuous when assessing reliability, but continuity of the process can be disrupted with appearance of random impulses. Thus, to more accurately assess software reliability, we proposed an OSS reliability model with SIDE. In the model, dynamic process of software fault is divided into a continuous and a skipped part, described the continuous part of the process with SDE, and described destruction of the continuity caused by unpredictable random events with random impulses. Finally, the proposed model is verified with two datasets from real OSS project, and the results show that the proposed model is more in line with reality and has better fitting effect than the existing models.

Multi-release is critical for modern open source software product in order to satisfy more customer requirements. Masked data, a kind of missing data, is the system failure data when the exact cause of the failures might be unknown. That is, the cause of the system failures may be any one of the objects. However, due to the influence of the test strategy in real project, the cause of the system failures may be a subset of the system objects, not any one of the objects. In this paper, the mathematical description of general masked data is presented based on the traditional masked data. Furthermore, a novel multi-release open source software (OSS) reliability model based on general masked data is proposed. Different from traditional multi-release OSS reliability model, the proposed approach is based on additive model with general masked data other than change point model. And then, the maximum likelihood estimation (MLE) process of the model parameters is derived in detail, and expectation maximization (EM) algorithm is used to solve the extremely complicated problem of the log-likelihood function. Finally, two data sets from real open source software project are applied to the proposed approach, and the results show that the proposed reliability model is useful and powerful.

Masked data are the system failure data when the exact cause of the failures might be unknown. That is, the cause of the system failures may be any one of the components. Additionally, to incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes have attracted widespread research attention recently. However, stochastic fault correction time and masked data brings more difficulties in parameter estimation. In this paper, a framework of open source software growth reliability model with masked data considering both fault detection and correction processes is proposed. Furthermore, a novel Expectation Least Squares (ELS) method, an EM-like (Expectation Maximization) algorithm, is used to solve the problem of parameter estimation, because of its mathematical convenience and computational efficiency. It is note that the ELS procedure is easy to use and useful for practical applications, and it just needs more relaxed hidden assumptions. Finally, three data sets from real open source software project are applied to the proposed framework, and the results show that the proposed reliability model is useful and powerful.