Supporting reliability engineers in exploiting the power of Dynamic Bayesian Networks

In this paper, we present an approach to reliability modeling and analysis based on the automatic conversion of a particular reliability engineering model, the Dynamic Fault Tree (DFT), into Dynamic Bayesian Networks (DBN). The approach is implemented in a software tool called RADYBAN (Reliability Analysis with DYnamic BAyesian Networks). The aim is to provide a familiar interface to reliability engineers, by allowing them to model the system to be analyzed with a standard formalism; however, a modular algorithm is implemented to automatically compile a DFT into the corresponding DBN. In fact, when the computation of specific reliability measures is requested, classical algorithms for the inference on Dynamic Bayesian Networks are exploited, in order to compute the requested parameters. This is performed in a totally transparent way to the user, who could in principle be completely unaware of the underlying Bayesian Network. The use of DBNs allows the user to be able to compute measures that are not directly computable from DFTs, but that are naturally obtainable from DBN inference. Moreover, the modeling capabilities of a DBN, allow us to extend the basic DFT formalism, by introducing probabilistic dependencies among system components, as well as the definition of specific repair policies that can be taken into account during the reliability analysis phase. We finally show how the approach operates on some specific examples, by describing the advantages of having available a full inference engine based on DBNs for the requested analysis tasks.     

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.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

NHPP software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage

In this paper, we propose a testing-coverage software reliability model that considers not only the imperfect debugging (ID) but also the uncertainty of operating environments based on a non-homogeneous Poisson process (NHPP). Software is usually tested in a given control environment, but it may be used in different operating environments by different users, which are unknown to the developers. Many NHPP software reliability growth models (SRGMs) have been developed to estimate the software reliability measures, but most of the underlying common assumptions of these models are that the operating environment is the same as the developing environment. But in fact, due to the unpredictability of the uncertainty in the operating environments for the software, environments may considerably influence the reliability and software's performance in an unpredictable way. So when a software system works in a field environment, its reliability is usually different from the theory reliability, and also from all its similar applications in other fields. In this paper, a new model is proposed with the consideration of the fault detection rate based on the testing coverage and examined to cover ID subject to the uncertainty of operating environments. We compare the performance of the proposed model with several existing NHPP SRGMs using three sets of real software failure data based on seven criteria. Improved normalized criteria distance (NCD) method is also used to rank and select the best model in the context of a set of goodness-of-fit criteria taken all together. All results demonstrate that the new model can give a significant improved goodness-of-fit and predictive performance. Finally, the optimal software release time based on cost and reliability requirement and its sensitivity analysis are discussed.     

A General Class of Change Point and Change Curve Modeling for Life Time Data

Change point hazard rate models arise in many life time data analysis, for example, in studying times until the undesirable side effects occur in clinical trials. In this paper we propose a general class of change point hazard model for survival data. This class includes and extends different types of change point models for survival data, e.g. cure rate model and lag model. Most classical approach develops estimates of model parameters, with particular interest in change point parameter and often the whole hazard function, but exclusively in terms of asymptotic properties. We propose a Bayesian approach, avoiding asymptotics and provide inference conditional upon the observed data. The proposed Bayesian models are fitted using Markov chain Monte Carlo method. We illustrate our proposed methodology with an application to modeling life times of the printed circuit board.     

Reliability analysis of a consecutive r-out-of-n: F system based on neural networks

In this paper, we present a generalized Markov reliability and fault-tolerant model, which includes the effects of permanent fault and intermittent fault for reliability evaluations based on neural network techniques. The reliability of a consecutive r-out-of-n: F system was obtained with a three-layer connected neural network represents a discrete time state reliability Markov model of the system. Such that we fed the neural network with the desired reliability of the system under design. Then we extracted the parameters of the system from the neural weights at the convergence of the neural network to the desired reliability. Finally, we obtain simulation results.     

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.     

基于MCMC模拟方法的带变点的NHPP软件可靠性模型

本文主要讨论软件测试过程中NHPP模型参数发生变化的情形,并用Bayes方法对GGO模型进行变点分析,运用基于Gibbs抽样的MCMC方法模拟出参数后验分布的马尔科夫链,最后借助于BUGS软件包对软件故障数据集Musa进行建模仿真,其结果表明该模型在软件可靠性变点分析中的直观性和有效性。     

失效率的综合E-Bayes估计

该文提出了可靠性参数的一种新估计方法综合E-Bayes估计法.在无失效数据情形下给出了失效率的E-Bayes估计的定义,并给出了失效率的E-Bayes估计。在引进失效信息后，给出了失效率的E-Bayes估计，并在此基础上给出了失效率和其它参数的综合E-Bayes估计。最后，结合实际问题进行计算，结果表明该文提出的方法可行且便于应用。     

Bayesian analysis of lymphatic spreading patterns in cancer of the thoracic esophagus

For the treatment of patients with cancer of the thoracic esophagus, lymphatic spreading is one important factor to infer how advanced their cancer is. We introduced a one-dimensional scale based on lymphatic spreading patterns, the stage of cancer, to express how advanced their cancer is, and we proposed a method to infer each patient's stage from his lymphatic spreading pattern by applying a Bayesian model. Our Bayesian model was built based on the assumption that lymphatic spreading in cancer could be explained as what was brought about by the advance of stage. In the modeling, we introduced the probability of what stage each patient was in as a prior distribution. We also introduced distribution functions of Weibull distributions to express the relation between the advance of stage and the increase of the probability of metastasis. Our model was applied to the data of nodal involvement obtained from 103 patients with cancer of the thoracic esophagus and the parameters were estimated with the maximum likelihood method. AIC was used to check that the data had enough information to be divided into the stages of a clinically reasonable number. With the estimated parameters, we inferred the probability of metastasis to each lymph node in each stage and calculated by Bayes' theorem with 31 new patients the probability of what stage they were in. The results well represented some characteristics of the lymphatic spreading and suggested the appropriateness of our approach.The present study was carried out under the ISM Cooperative Research Program (91-ISM·CRP-18).     

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In this paper, we investigate a competing risks model based on exponentiated Weibull distribution under Type-I progressively hybrid censoring scheme. To estimate the unknown parameters and reliability function, the maximum likelihood estimators and asymptotic confidence intervals are derived. Since Bayesian posterior density functions cannot be given in closed forms, we adopt Markov chain Monte Carlo method to calculate approximate Bayes estimators and highest posterior density credible intervals. To illustrate the estimation methods, a simulation study is carried out with numerical results. It is concluded that the maximum likelihood estimation and Bayesian estimation can be used for statistical inference in competing risks model under Type-I progressively hybrid censoring scheme.     

Truncated software reliability growth model

Due to the large scale application of software systems, software reliability plays an important role in software developments. In this paper, a software reliability growth model (SRGM) is proposed. The testing time on the right is truncated in this model. The instantaneous failure rate, mean-value function, error detection rate, reliability of the software, estimation of parameters and the simple applications of this model are discussed.     

Bayesian estimation for generalized exponential distribution based on progressive type-I interval censoring

In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley’s approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.     

治愈率模型在屏蔽数据可靠性分析中的应用研究

针对传统方法中的不足,在引入标准治愈率模型的基础上,提出在屏蔽数据可靠性分析中应用一种扩展的治愈率模型的建模方法;分析证明了利用该方法进行建模分析时仅需对模型作较少的前提假设,在信息不足的情况下能够识别出伴随变量对系统寿命分布的影响,进而有效提高模型估计的稳健性.通过运用基于Gibbs抽样的MCMC方法动态模拟出相关参数后验分布的马尔可夫链,给出随机截尾条件下模型参数的贝叶斯估计;实例分析的结果,证明了该模型在可靠性应用中的直观性与有效性.     

Using Bayesian networks to improve fault diagnosis during manufacturing tests of mobile telephone infrastructure

Intense competition and the requirement to continually drive down costs within a mature mobile telephone infrastructure market calls for new and innovative solutions to process improvement. One particular challenge is to improve the quality and reliability of the diagnostic process for systems testing of Global System for Mobile Communications and Universal Mobile Telecommunications System products. In this paper, we concentrate on a particularly important equipment type—the Base Transceiver Station (BTS). The BTS manages the radio channels and transfers signalling information to and from mobile stations (ie mobile phones). Most of the diagnostic processes are manually operated and rely heavily on individual operators and technicians' knowledge for their performance. Hence, there is a high cost associated with troubleshooting in terms of time and manpower. In this paper, we employ Bayesian networks (BNs) to model the domain knowledge that comprises the operations of the System Under Test, Automated Test Equipment (ATE), and the diagnostic skill of experienced engineers, in an attempt to enhance the efficiency and reliability of the diagnostic process. The proposed automated diagnostic tool (known as Wisdom) consists of several modules. An intelligent user interface provides possible solutions to test operators/technicians, captures their responses, and activates the automated test program. Server and client software architecture is used to integrate Wisdom with the ATE seamlessly and to maintain Wisdom as an independent module. A local area network provides the infrastructure for managing and deploying the multimedia information in real time. We describe how a diagnostic model can be developed and implemented using a BN approach. We also describe how the resulting process of diagnosis following failure, advice generation, and subsequent actions by the operator are handled interactively by the prototype system. The results from an initial survey are presented, indicating sizeable reductions in fault correction times for many fault types.     

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.     

无失效数据情形可靠性参数的估计和调整

本文在无失效取样情形下,提出了产品可靠性参数的一种估计和调整的方法———加权多层Bayes估计法.在无失效数据情形下失效率的多层Bayes估计和引进失效信息后失效率的多层Bayes估计的基础上,对可靠性参数进行了估计和调整———给出了失效率和可靠度的加权多层Bayes估计.最后,结合发动机的实际问题进行了计算,结果表明本文提出的方法可行且便于应用.     

某型工程车系统可靠性分析

本应用失效树分析法,以某型工程车进行了可靠性分析,建立了该系统的失效树,在此基础上用最小割集法和系统失效树的可靠性仿真法计算了该系统的可靠性参数,并对一些结果进行了比较。     

Single-use reliability computation of a semi-Markovian system

Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first and second moments of the single-use reliability. The model and the validity of the results are illustrated through a numerical example.     

Duane-LR模型下复杂系统的动态可靠性增长评定

基于复杂系统可靠性增长试验的特点，运用Duane可靠性增长模型结合数理统计中的线性回归方法对新批次产品的可靠性参数进行预测。结合产品的少量现场试验数据，利用Bayes方法对系统的可靠性增长试验结果进行评定。文中首先给出了可靠性增长分析的模型，然后运用历次阶段试验中的可靠性增长数据建立动态参数的递推估计模型，在此基础上，运用随机变量函数的分布，给出各阶段可靠性增长试验中可靠性参数的Bayes估计。文中对Weibull、指数和二项分布三种试验结果进行分析，给出计算公式。