We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

A survey of maintenance policies of deteriorating systems

Technical foundations introduction software reliability and system reliability the operational profile software reliability modelling survey model evaluation and recalibration techniques practices and experiences best current practice of SRE software reliability measurement experience measurement-based analysis of software reliability software fault and failure classification techniques trend analysis in validation and maintenance software reliability and field data analysis software reliability process assessment emerging techniques software reliability prediction metrics software reliability and testing fault-tolerant SRE software reliability using fault trees software reliability process simulation neural networks and software reliability. Appendices: software reliability tools software failure data set repository.

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Handbook of software reliability engineering

A number of analytical models have been proposed during the past 15 years for assessing the reliability of a software system. In this paper we present an overview of the key modeling approaches, provide a critical analysis of the underlying assumptions, and assess the limitations and applicability of these models during the software development cycle. We also propose a step-by-step procedure for fitting a model and illustrate it via an analysis of failure data from a medium-sized real-time command and control software system.

Software Reliability Models: Assumptions, Limitations, and Applicability

This paper provides: an overview of the methods that have been developed since 1977 for solving various reliability optimization problems; applications of these methods to various types of design problems; and heuristics, metaheuristic algorithms, exact methods, reliability-redundancy allocation, multi-objective optimization and assignment of interchangeable components in reliability systems. Like other applications, exact solutions for reliability optimization problems are not necessarily desirable because exact solutions are difficult to obtain, and even when they are available, their utility is marginal. A majority of the work in this area is devoted to developing heuristic and metaheuristic algorithms for solving optimal redundancy-allocation problems.

An annotated overview of system-reliability optimization

This paper investigates a stochastic model for a software error detection process in which the growth curve of the number of detected software errors for the observed data is S-shaped. The software error detection model is a nonhomogeneous Poisson process where the mean-value function has an S-shaped growth curve. The model is applied to actual software error data. Statistical inference on the unknown parameters is discussed. The model fits the observed data better than other models.

S-Shaped Reliability Growth Modeling for Software Error Detection

The s-shaped growth curves of detected software errors can be observed in software testing. The delayed s-shaped and inflection s-shaped software reliability growth models based on a nonhomogeneous Poisson process are discussed. The software reliability growth types of the models are investigated in terms of the error detection rate per error. In addition, a viable method for the software quality assessment, which integrates the capture-recapture method and the models above, is discussed, and its application to actual test data is illustrated.

s-Shaped Software Reliability Growth Models and Their Applications

Many software reliability growth models have been proposed in the past decade. Those models tacitly assume that testing-effort expenditures are constant throughout software testing. This paper develops realistic software reliability growth models incorporating the effect of testing-effort. The software error detection phenomenon in software testing is modeled by a nonhomogeneous Poisson process. The software reliability assessment measures and the estimation methods of parameters are investigated. Testing-effort expenditures are described by exponential and Rayleigh curves. Least-squares estimators and maximum likelihood estimators are used for the reliability growth parameters. The software reliability data analyses use actual data. The software reliability growth models with testing-effort can consider the relationship between the software reliability growth and the effect of testing-effort. Thus, the proposed models will enable us to evaluate software reliability more realistically.

Software Reliability Growth Models with Testing-Effort

Software reliability measurement during the testing phase is essential for examining the degree of quality or reliability of a developed software system. A software-reliability growth model incorporating the amount of test effort expended during the software testing phase is developed. The time-dependent behavior of test-effort expenditures is described by a Weibull curve. 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 Poission process. Using the model, the method of data analysis for software reliability measurement is developed. This model is applied to the prediction of additional test-effort expenditures to achieve the objective number of errors detected by software testing, and the determination of the optimum time to stop software testing for release. >

Software-reliability growth with a Weibull test-effort: a model and application

In general it is considered to be unrealistic in software reliability modelling to assume that the faults detected by software testing are perfectly removed without introducing new faults. In this paper we propose two software reliability assessment models with imperfect debugging by assuming that new faults are sometimes introduced when the faults originally latent in a software system are corrected and removed during the testing phase. It is assumed that the fault detection rate is proportional to the sum of the numbers of faults remaining originally in the system and faults introduced by imperfect debugging. These two models are described by a nonhomogeneous Poisson process. Several quantitative measures for reliability assessment are derived, and the maximum likelihood estimations of unknown model parameters are presented. Finally, numerical examples of software reliability analysis based on these two models are shown.

Shigeru Yamada

Papers

S-Shaped Reliability Growth Modeling for Software Error Detection

s-Shaped Software Reliability Growth Models and Their Applications

Software Reliability Growth Models with Testing-Effort

Software-reliability growth with a Weibull test-effort: a model and application

Imperfect debugging models with fault introduction rate for software reliability assessment