In this paper, we propose a Markov chain-based testability growth model (TGM) for the just in-time fix program. This model can help the system designers to manage the testability growth process during system maturation. We also derive a cost-benefit model for allocating test resources to optimize a specified testability metric subject to a constraint on cumulative test cost. Bayesian inference, coupled with a hybrid genetic and particle swarm optimization method, is used to estimate the parameters of the TGM from evolving data, and the resulting model is utilized to track and project the testability metric. A near-optimal Lagrangian relaxation-based algorithm is applied to solve the test resource allocation problem. The testability growth and resource allocation models are validated via simulation examples. Results show that the model and algorithms presented in this paper have the potential to efficiently manage the testability growth problem.

A Markov Chain-Based Testability Growth Model With a Cost-Benefit Function

Problems of making inferences about abrupt changes in the mechanism underlying a sequence of observations are considered in both retrospective and on-line contexts. Among the topics considered are the Lindisfarne scribes problem; switching straight lines; manoeuvering targets, and shifts of level or slope in linear time series models. Summary analyses of data obtained in studies of schizophrenic and kidney transplant patients are presented.

Change-Point problems: approaches and applications

A fully Bayes approach is presented for analyzing product reliability during the development phase. Based on a Bayes version of the Barlow-Scheuer reliability-growth model, it is assumed that the product goes through a series of test/modification stages, where each product test yields attribute (pass-fail) data, and failure types are classified as fixable or nonfixable. Relevant information on both the failure probabilities and the reliability-growth process is used to motivate the prior joint distribution for the probability of each failure type over the specified range of testing. Results at a particular test-stage can be used to update the knowledge about the probability of each failure type (and thus product reliability) at the current test-stage as well as at subsequent test-stages, and at the end of the development phase. A relative ease of incorporation of prior information and a tractability of the posterior analysis are accomplished by using a Dirichlet distribution as the prior distribution for a transformation of the failure probabilities. >

A Bayes method for assessing product-reliability during development testing

Survival models used in biomedical and reliability contexts typically involve data censoring, and may also involve constraints in the form of ordered parameters. In addition, inferential interest often focuses on non-linear functions of natural model parameters. From a Bayesian statistical analysis perspective, these features combine to create difficult computational problems by seeming to require (multi-dimensional) numerical integrals over awkwardly defined regions. This paper illustrates how these apparent difficulties can be overcome, in both parametric and nonparametric settings, by the Gibbs sampler approach to Bayesian computation.

Bayesian Computations in Survival Models Via the Gibbs Sampler

In this article, we consider the development and analysis of both attribute- and variable-data reliability growth models from a Bayesian perspective. We begin with an overview of a Bayesian attribute-data reliability growth model and illustrate how this model can be extended to cover the variable-data growth models as well. Bayesian analysis of these models requires inference over ordered regions, and even though closed-form results for posterior quantities can be obtained in the attribute-data case, variable-data models prove difficult. In general, when the number of test stages gets large, computations become burdensome and, more importantly, the results may become inaccurate due to computational difficulties. We illustrate how the difficulties in the posterior and predictive analyses can be overcome using Markov-chain Monte Carlo methods. We illustrate the implementation of the proposed models by using examples from both attribute and variable reliability growth data.

https://www.jstor.org/stable/pdfplus/1271389.pdf

Bayesian computations for a class of reliability growth models

The problem of estimating the reliability of a system which is undergoing development testing is considered from a Bayesian standpoint. Formally, m sets of binomial trials are performed under conditions which lead to an ordering, ?1 < ?2 < ... < ?m, of the binomial parameters. The parameter of interest is ?m, the final underlying reliability of the system. The marginal posterior pdf for ?m is easily obtained when uniform prior pdf's are assumed. The method is illustrated.

A.F.M. Smith

Papers

A Bayesian Note on Reliability Growth During a Development Testing Program