A Markov modulated Poisson model for software reliability

In this paper, we consider a latent Markov process governing the intensity rate of a Poisson process model for software failures. The latent process enables us to infer performance of the debugging operations over time and allows us to deal with the imperfect debugging scenario. We develop the Bayesian inference for the model and also introduce a method to infer the unknown dimension of the Markov process. We illustrate the implementation of our model and the Bayesian approach by using actual software failure data.     

A markov process model for software reliability analysis

Software reliability is a rapidly developing discipline. In this paper we model the fault-detecting processes by Markov processes with decreasing jump intensity. The intensity function is suggested to be a power function of the number of the remaining faults in the software. The models generalize the software reliability model suggested by Jelinski and Moranda (‘Software reliability research’, in W. Freiberger (ed.), Statistical Computer Performance Evaluation, Academic Press, New York, 1972. pp. 465–497). The main advantage of our models is that we do not use the assumption that all software faults correspond to the same failure rate. Preliminary studies suggest that a second-order power function is quite a good approximation. Statistical tests also indicate that this may be the case. Numerical results show that the estimation of the expected time to next failure is both reasonable and decreases relatively stably when the number of removed faults is increased.     

Optimal allocation policies for testing-resource based on a software reliability growth model

A lot of development resources are consumed during the software testing phase fundamentally consisting of module testing, integration, testing and system testing. Then, it is of great importance for a manager to decide how to effectively spend testing-resources on software testing for developing a quality and reliable software.In this paper, we consider two kinds of software testing-resource allocation problems to make the best use of the specified testing-resources during module testing. Also, we introduce a software reliability growth model for describing the time-dependent behavior of detected software faults and testing-resource expenditures spent during the testing, which is based on a nonhomogeneous Poisson process. It is shown that the optimal allocation of testing-resources among software modules can improve software reliability.     

Flexible software reliability growth model with testing effort dependent learning process

A lot of importance has been attached to the testing phase of the Software Development Life Cycle (SDLC). It is during this phase it is checked whether the software product meets user requirements or not. Any discrepancies that are identified are removed. But testing needs to be monitored to increase its effectiveness. Software Reliability Growth Models (SRGMs) that specify mathematical relationships between the failure phenomenon and time have proved useful. SRGMs that include factors that affect failure process are more realistic and useful. Software fault detection and removal during the testing phase of SDLC depend on how testing resources (test cases, manpower and time) are used and also on previously identified faults. With this motivation a Non-Homogeneous Poisson Process (NHPP) based SRGM is proposed in this paper which is flexible enough to describe various software failure/reliability curves. Both testing efforts and time dependent fault detection rate (FDR) are considered for software reliability modeling. The time lag between fault identification and removal has also been depicted. The applicability of our model is shown by validating it on software failure data sets obtained from different real software development projects. The comparisons with established models in terms of goodness of fit, the Akaike Information Criterion (AIC), Mean of Squared Errors (MSE), etc. have been presented.     

A modified Markov model for the estimation of computer software performance

The model proposed by Trivedo and Shooman [8] is extended and modified by assuming that (1) the error occurrence rate when the machine is running is proportional to the number of errors in the system; (2) the error correction rate has two components, either an error is corrected with correction rate μ₀ or an error is corrected but a new error is created with ineffective correction rate μ₁. The solution of the differential equations corresponding to the model is obtained in closed form.     

Enhancing software reliability modeling and prediction through the introduction of time-variable fault reduction factor

Over the past three decades, many software reliability models with different parameters, reflecting various testing characteristics, have been proposed for estimating the reliability growth of software products. We have noticed that one of the most important parameters controlling software reliability growth is the fault reduction factor (FRF) proposed by Musa. FRF is generally defined as the ratio of net fault reduction to failures experienced. During the software testing process, FRF could be influenced by many environmental factors, such as imperfect debugging, debugging time lag, etc. Thus, in this paper, we first analyze some real data to observe the trends of FRF, and consider FRF to be a time-variable function. We further study how to integrate time-variable FRF into software reliability growth modeling. Some experimental results show that the proposed models can improve the accuracy of software reliability estimation. Finally, sensitivity analyses of various optimal release times based on cost and reliability requirements are discussed. The analytic results indicate that adjusting the value of FRF may affect the release time as well as the development cost.     

A discrete time model for software reliability with application to a flight control software

This work is motivated by a particular software reliability problem in a unit of flight control software developed by the Indian Space Research Organization (ISRO), in which the testing of the software is carried out in multiple batches, each consisting of several runs. As the errors are found during the runs within a batch, they are noted, but not debugged immediately; they are debugged only at the end of that particular batch of runs. In this work, we introduce a discrete time model suitable for this type of periodic debugging schedule and describe maximum likelihood estimation for the model parameters. This model is used to estimate the reliability of the software. We also develop a method to determine the additional number of error‐free test runs required for the estimated reliability to achieve a specific target with some high probability. We analyze the test data on the flight control software of ISRO. Copyright © 2011 John Wiley & Sons, Ltd.     

A Practical Sequential Stopping Rule for High-Dimensional Markov Chain Monte Carlo

A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation when the computational uncertainty is small relative to the posterior uncertainty. Further, we show this stopping rule is equivalent to stopping when the effective sample size is sufficiently large. Such a stopping rule has previously been shown to work well in settings with posteriors of moderate dimension. In this article, we illustrate its utility in high-dimensional simulations while overcoming some current computational issues. As examples, we consider two complex Bayesian analyses on spatially and temporally correlated datasets. The first involves a dynamic space-time model on weather station data and the second a spatial variable selection model on fMRI brain imaging data. Our results show the sequential stopping rule is easy to implement, provides uncertainty estimates, and performs well in high-dimensional settings. Supplementary materials for this article are available online.