In this paper, we present a software gain model under random field environment with consideration of not only time to remove faults during in-house testing, cost of removing faults during beta testing, risk cost due to software failure, but also the benefits from reliable executions of the software during the beta testing and field operation. To our knowledge, this is the first study that incorporates the random field environmental factor into the cost model. We also provide an optimal release policy in which the net gain of the software development process is maximized. This gain model can help managers and developers to determine when to stop testing the software and release it to beta testing users and to end-users.

Software reliability growth models (SRGMs) have been developed to estimate software reliability measures such as the number of remaining faults, software failure rate, and software reliability. Issues such as imperfect debugging and the learning phenomenon of developers have been considered in these models. However, most SRGMs assume that faults detected during tests will eventually be removed. Consideration of fault removal efficiency in the existing models is limited. In practice, fault removal efficiency is usually imperfect. This paper aims to incorporate fault removal efficiency into software reliability assessment. Fault removal efficiency is a useful metric in software development practice and it helps developers to evaluate the debugging effectiveness and estimate the additional workload. In this paper, imperfect debugging is considered in the sense that new faults can be introduced into the software during debugging and the detected faults may not be removed completely. A model is proposed to integrate fault removal efficiency, failure rate, and fault introduction rate into software reliability assessment. In addition to traditional reliability measures, the proposed model can provide some useful metrics to help the development team make better decisions. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power. The expected number of residual faults and software failure rate are also presented.

This paper presents a NHPP-based SRGM (software reliability growth model) for NVP (N-version programming) systems (NVP-SRGM) based on the NHPP (nonhomogeneous Poisson process). Although many papers have been devoted to modeling NVP-system reliability, most of them consider only the stable reliability, i.e., they do not consider the reliability growth in NVP systems due to continuous removal of faults from software versions. The model in this paper is the first reliability-growth model for NVP systems which considers the error-introduction rate and the error-removal efficiency. During testing and debugging, when a software fault is found, a debugging effort is devoted to remove this fault. Due to the high complexity of the software, this fault might not be successfully removed, and new faults might be introduced into the software. By applying a generalized NHPP model into the NVP system, a new NVP-SRGM is established, in which the multi-version coincident failures are well modeled. A simplified software control logic for a water-reservoir control system illustrates how to apply this new software reliability model. The s-confidence bounds are provided for system-reliability estimation. This software reliability model can be used to evaluate the reliability and to predict the performance of NVP systems. More application is needed to validate fully the proposed NVP-SRGM for quantifying the reliability of fault-tolerant software systems in a general industrial setting. As the first model of its kind in NVP reliability-growth modeling, the proposed NVP SRGM can be used to overcome the shortcomings of the independent reliability model. It predicts the system reliability more accurately than the independent model and can be used to help determine when to stop testing, which is a key question in the testing and debugging phase of the NVP system-development life cycle.