Realistic assessments of the reliability of networked systems, series and parallel systems being special cases, require that we account for interdependence between the component life-lengths. The key to doing this is the specification and use of a suitable probability model in two or more dimensions. Consequently, several multivariate probabilistic models have been proposed in the literature. Many of these models have marginal distributions that are exponential; the ones by Gumbel, and by Marshall and Olkin being some of the earliest and the best known. The purpose of this paper is two fold: The first purpose is to articulate the nature of dependence encapsulated by such models, using a perspective which is best appreciated by a user. Specifically, we anchor on the bivariate case, and focus attention on the conditional mean as a measure of dependence. The second purpose, motivated by the first, is to introduce a new family of multivariate distributions with exponential marginals, whose conditional mean fills a void in the general forms of the conditional means of the available models. The method of "copulas" is used to generate this new family of distributions. Attention is focused on the case of exponential marginals, because the notion of "hazard potentials" enables us to use multivariate distributions with exponential marginals as a seed for generating multivariate distributions with marginals other than the exponential.

As science and technology become increasingly sophisticated, government and industry are relying more and more on science's advanced methods to determine reliability. Unfortunately, political, economic, time, and other constraints imposed by the real world, inhibit the ability of researchers to calculate reliability efficiently and accurately. Because of such constraints, reliability must undergo an evolutionary change. The first step in this evolution is to re-interpret the concept so that it meets the new century's needs. The next step is to quantify reliability using both empirical methods and auxiliary data sources, such as expert knowledge, corporate memory, and mathematical modeling and simulation.

The concatenation of failure rate functions results in point process models that need not possess independent increments, or lack memory features of Poisson processes. Processes having a memory are more realistic as compared to those that do not, and as a consequence provide a credible framework for tracking reliability and predicting failure times. The purpose of the paper is to propose and describe a model for software reliability based on this paradigm. The proposed model is adaptive, can explain empirically observed phenomena, and outperforms the predictive ability of its competitors. The model and its inferential mechanism are complex, but software to implement it with ease, is available.

We propose a Bayesian approach for predicting the number of failures in a piece of software, using the logarithmic-Poisson model, a nonhomogeneous Poisson process (NHPP) commonly used for describing software failures. A similar approach can be applied to other forms of the NHPP. The key feature of the approach is that now we are able to use, in a formal manner, expert knowledge on software testing, as for example, published information on the empirical experiences of other researchers. This is accomplished by treating such information as expert opinion in the construction of a likelihood function which leads us to a joint distribution. The procedure is computationally intensive, but for the case of the logarithmic-Poisson model has been codified for use on a personal computer. We illustrate the working of the approach via some real live data on software testing. The aim is not to propose another model for software reliability assessment. Rather, we present a methodology that can be invoked with existing software reliability models.>

A method for projecting software productivity with reasonable accuracy which uses the statistical techniques of time series analysis is described. The measure of productivity is the development time required per line of code. In making productivity projections, the key issue is the need to achieve a balance between forecasting stability and responsiveness to changing conditions. An integrated moving average process of order one, using exponential smoothing of all the previous observations, is judged appropriate for software productivity analysis, particularly where there are limited data available or where conditions are sufficiently varied to make much of the available data inapplicable. Empirical evidence suggests that most commonly encountered time series can be reasonably well described by such methods. The methods for computing the weights used for exponential smoothing are described, as are the means for determining prediction intervals, or measures of forecast uncertainty. This data analytic approach uses historical data alone, unlike structural methods where learning curves as well as prior data are used to define the predictive process.>

A decision-theoretic procedure for determining an optimal time interval for testing software prior to its release is proposed. The approach is based on the principles of decision-making under uncertainty and involves a maximization of expected utility. Two plausible forms for the utility function, one based on costs and the other involving the realized reliability of the software, are described. Using previous results on probabilistic models for software failure, the ensuing optimization problem (which can be addressed using numerical techniques) is outlined for the case of single-state testing. The sensitivity of the results to the various input parameters is discussed, and some directions for future research are outlined.>

In this paper we motivate a random coefficient autoregressive process of order 1 for describing reliability growth or decay. We introduce several ramifications of this process, some of which reduce it to a Kalman Filter model. We illustrate the usefulness of our approach by applying these processes to some real life data on software failures. Finally, we make a pairwise comparison of the models in terms of the ratio of likelihoods of their predictive distributions, and identify the "best" model.