In general, the software reliability models based on the nonhomogeneous Poisson processes (NHPPs) are quite popular to assess quantitatively the software reliability and its related dependability measures. Nevertheless, it is not so easy to select the best model from a huge number of candidates in the software testing phase, because the predictive performance of software reliability models strongly depends on the fault-detection data. The asymptotic trend of software fault-detection data can be explained by two kinds of NHPP models; finite fault model and infinite fault model. In other words, one needs to make a hypothesis whether the software contains a finite or infinite number of faults, in selecting the software reliability model in advance. In this article, we present an approach to treat both finite and infinite fault models in a unified modeling framework. By introducing an infinite server queueing model to describe the software debugging behavior, we show that it can involve representative NHPP models with a finite and an infinite number of faults. Further, we provide two parameter estimation methods for the unified NHPP based software reliability models from both standpoints of Bayesian and nonBayesian statistics. Numerical examples with real fault-detection data are devoted to compare the infinite server queueing model with the existing one under the same probability circumstance.

The article gives detailed mathematical results on the hypergeometric distribution software reliability model (HGDSRM) proposed by Y. Tohma et al. (1989; 1991). In the above papers, Tohma et al. developed the HGDSRM as a discrete-time stochastic model and derived a recursive formula for the mean cumulative number of software faults detected up to the i-th (>0) test instance in testing phase. Since their model is based on only the mean value of the cumulative number of faults, it is impossible to estimate not only the software reliability but also the other probabilistic dependability measures. We introduce the concept of cumulative trial processes, and describe the dynamic behavior of the HGDSRM exactly. In particular, we derive the probability mass function of the number of software faults detected newly at the i-th test instance and its mean as well as the software reliability defined as the probability that no faults are detected up to an arbitrary time. In numerical examples with real software failure data, we compare several HGDSRMs with different model parameters in terms of least squared sum and show that the mathematical results obtained here are very useful to assess the software reliability with the HGDSRM.

We consider the issue of bulk loading large data sets for the UB-Tree, a multidimensional index structure. Especially in data warehousing (DW), data mining and OLAP it is necessary to have efficient bulk loading techniques, because loading occurs not continuously, but only from time to time with usually large data sets. We propose two techniques, one for initial loading, which creates a new UB-Tree, and one for incremental loading, which adds data to an existing UB-Tree. Both techniques try to minimize I/O and CPU cost. Measurements with artificial data and data of a commercial data warehouse demonstrate that our algorithms are efficient and able to handle large data sets. As well as the UB-Tree, they are easily integrated into a RDBMS.

The GMDH (group method of data handling) network is an adaptive learning machine based on the principle of heuristic self-organization. The authors apply the GMDH networks to predict software reliability in the testing phase. Three kinds of networks: the basic GMDH and its improved versions based on PSS (prediction sum of squared) and AIC (Akaike information criterion), are introduced for the prediction of the failure-occurrence times observed in the testing phase of the software system. In numerical examples, the GMDH networks, the usual MLP (multi-layer perceptron) neural networks and existing SRGMs (software reliability growth models) are compared from the view point of predictive performance. It is shown that the GMDH networks can overcome the problem of determining a suitable network size in the use of an MLP neural network, and can provide a more accurate measure in the software reliability assessment than other prediction devices. Further, the problem of determining the optimal software release schedule, which minimizes the relevant expected total software cost, is considered in the framework of the GMDH network architecture.

This paper considers two stochastic models for a file recovery action with checkpoint generations when two kinds of failures; system failure and media failure, occur according to a homogeneous Poisson process and a renewal process, respectively. For the unknown media failure time distribution, we develop statistical nonparametric algorithms to estimate the optimal checkpoint intervals which maximize the system availabilities. The algorithms proposed are based on the corresponding total time on test (TTT) statistics to the media failure time distribution, and can provide strongly consistent estimates from its sample data.

This article proposes an extended symmetric diffusion network that is applied to the design of synergetic computers. The state of a synergetic computer is translated to that of order parameters whose dynamics is described by a stochastic differential equation. The order parameter converges to the Boltzmann distribution, under some condition on the drift term, derived by the Fokker-Planck equation. The network can learn the dynamics of the order parameters from a nonlinear potential. This property is necessary to design the coefficient values of the synergetic computer. We propose a searching function for the image processing executed by the synergetic computer. It is shown that the image processing with the searching function is superior to the usual image-associative function of synergetic computation. The proposed network can be related, as a special case, to the discrete-state Boltzmann machine by some transformation. Finally, the extended symmetric diffusion network is applied to the estimation problem of an entire density function, as well as the proposed searching function for the image processing.

A software reliability growth model incorporating the amount of test effort expenditures during the software testing phase is described. The time-dependent behavior of test-effort expenditures is described by a Weibull curve due to the flexibility. Assuming that the error detection rate to the amount of test-effort spent during the testing phase is proportional to the current error content, the model is formulated by a nonhomogeneous Poisson process. Using this model, the method of data analysis for software reliability measurement is presented. Also, this model is applied to the prediction of additional test-effort expenditures to obtain the objective number of errors detected by software testing and the determination of the optimum time to stop software testing for release.>

This paper summarizes existing software reliability growth models (SRGM's) described by nonhomogeneous Poisson processes. The SRGM's are classified in terms of the software reliability growth index of the error detection rate per error. The maximum-likelihood estimations based on the SRGM's are discussed for software reliability data analysis and software reliability evaluation. Using actual software error data observed by software testing, application examples of the existing SRGM's are illustrated.