Two-stage Bayesian models—application to ZEDB project

Bunea, Cornel; Charitos, Theodore; Cooke, Roger M.; Becker, Günter

doi:10.1016/j.ress.2004.10.016

Cited by 15 publications

(19 citation statements)

References 8 publications

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“…Many think that any claim of defect-free software is unbelievable, on the basis of experience and of the usual complexity of software. On the other hand, large parts of the software engineering community (especially those studying and practicing "formal methods") point at it as a very feasible target 11 . We think that the case of a "perfect", "fault-free" design is actually plausible, especially for very simple software as required in some critical applications, and that reasoning about its probability (for the class of faults of interest, e.g.…”

Section: Probability Of Pfd =mentioning

confidence: 99%

“…Uncertainty propagation methods will in theory produce accurate results for any given distribution; but their application is hard: apart from computational complexity, their fundamental drawbacks are in delivering numerical results rather than insight on how the various aspects of parameter uncertainty may affect the results, and in requiring a complete description of the parameters' distribution, which in practice may be hard to specify with any degree of soundly based consensus (especially if we consider that the uncertainties on the various parameters are not statistically independent -a concern called sometimes "epistemic correlation"). When the problem is to extract a distribution for the parameters in question from detailed failure data about multiple similar systems, typical approaches to modelling and inference use hierarchical or empirical Bayes [3,Ch.8], [42,Ap.A], [11], [40, §6], [31].…”

Section: Introductionmentioning

confidence: 99%

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Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty

Strigini

Wright

2014

Reliability Engineering & System Safety

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When deciding whether to accept into service a new safety-critical system, or choosing between alternative systems, uncertainty about the parameters that affect future failure probability may be a major problem. This uncertainty can be extreme if there is the possibility of unknown design errors (e.g. in software), or wide variation between nominally equivalent components.We study the effect of parameter uncertainty on future reliability (survival probability), for systems required to have low risk of even only one failure or accident over the long term (e.g. their whole operational lifetime) and characterised by a single reliability parameter (e.g. probability of failure per demand -pfd ). A complete mathematical treatment requires stating a probability distribution for any parameter with uncertain value. This is hard, so calculations are often performed using point estimates, like the expected value.We investigate conditions under which such simplified descriptions yield reliability values that are sure to be pessimistic (or optimistic) bounds for a prediction based on the true distribution. Two important observations are: (i) using the expected value of the reliability parameter as its true value guarantees a pessimistic estimate of reliability, a useful property in most safety-related decisions; (ii) with a given expected pfd, broader distributions (in a formally defined meaning of "broader"), that is, systems that are a priori "less predictable", lower the risk of failures or accidents.Result (i) justifies the simplification of using a mean in reliability modelling; we discuss within which scope this justification applies, and explore related scenarios, e.g. how things improve if we can test the system before operation. Result (ii) offers more flexible ways of bounding reliability predictions, but also has important, often counter-intuitive implications for decision making in various areas, like selection of components, project management, and product acceptance or licensing. For instance, in regulatory decision making dilemmas may arise in which the goal of minimising risk runs counter to other commonly held priorities, like predictability of risk; in safety assessment using expert opinion, the commonly recognised risk of experts being "overconfident" may be less dangerous than their being under confident. 1 CSR TECHNICAL REPORT Contents IntroductionPredictions of reliability and safety through probabilistic modelling depend on the values of model parameters, e.g. component failure rates, which are often uncertain. The main application scenario that motivates our research involves decisions on accepting a software product for use in a safety critical application requiring low accident probability over the operational life of the system in which it is embedded. For instance, an explicit requirement in civil aviation is that "catastrophic failure conditions" be "so unlikely that they are not anticipated to occur during the entire operational life of all airplanes of one type" [16]. Nuclear power pro...

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Section: Probability Of Pfd =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty

Strigini

Wright

2014

Reliability Engineering & System Safety

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“…However, such a joint distribution would not be easy to derive in terms of the consideration of the possible correlations among a, a, and g. Since the expected number of all potential errors a obviously has no impact on a and g which denote the debugging and learning abilities of the testing staff, the relationship between a and g would be more essential in forming the joint distribution. Moreover, since the Gamma distribution has been used for research in the field of software reliability due to its flexibility and tractability (Cid and Achcar 1999;Ö zekici and Soyer 2003;Bunea et al 2005), the marginal distributions of a, a, and g are assumed to be Gamma distributed in this study, and a bivariate gamma distribution proposed by Moran (1969) is especially employed to deliberate the correlation between a and g. As a result, the joint prior distribution of a, a, and g could be presented as follows:…”

Section: Bayesian Approachmentioning

confidence: 99%

Bayesian updating of optimal release time for software systems

Chiu

Huang

2008

Software Qual J

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In this paper, a Bayesian method dealing with software reliability growth with consideration of the learning effect is proposed to determine an optimal release time for software systems with regard to the testing cost and experts' prior judgments. Such an approach is able to devise an appropriate software-debugging scheme which has the best arrangement of available resources and personnel with a minimal software testing cost when lacking sufficient information for decision making. Past research on software reliability emphasized the estimation of the number of cumulative software errors or the software reliability with respect to a specific time period, yet it neglected the determination of software release time with consideration of the software testing cost, meaning that existing approaches are not entirely practical. Accordingly, the proposed method is concerned with the evaluation of the software testing cost incurred during the testing period based on experts' prior judgments and the software testing data collected within a given duration, and is thus characterized by its practicality as well as meaningfulness with consideration of the learning effect. Finally, a numerical example is given to verify the effectiveness of the proposed approach, and sensitivity and risk analyses are performed on this example.

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“…The objective is to assimilate data from different sources in order to overcome either conflicting data, or a general paucity of data, as is typically the case for failure data in very reliable systems. Bunea et al (2005) consider the case of n different nuclear facilities each having their own failure data sets with each facility trying to enhance its decision making by benefiting from the 'lessons learned' at other facilities. Twostage models, originally known as hierarchical Bayes models, are also used by Hofer (1999) to model initiating events in large industrial processes.…”

Section: Condition Statesmentioning

confidence: 99%

“…But this does not mean that the posterior hyper-pdf f (α|x) will become peaked itself. Rather, the prior pdf of the hyper-parameters will continue to 'persist' (Bunea et al 2005). A typical example occurs when the hyper-parameters are discretized and even if an infinite sample of X becomes available, then the posterior probabilities associated with different values of α will indeed stabilize but they will never converge to either zero or one (Maes 2002).…”

Section: Two-stage Bayesian Models For Exchangeable Csmentioning

confidence: 99%

A comparison of one-stage and two-stage Bayesian processes in engineering decision-making

Maes

Dann

2007

Civil Engineering and Environmental Systems

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Engineering decision-making problems often involve conditions that vary spatially either in a continuous way or from element to element. In such cases, the use of two-stage Bayesian models is often advisable in design optimization, maintenance and inspection planning. Two-stage models are based on a 'state' or 'condition' variable vector that is assumed to be conditionally independent with a pdf given a set of 'hyper-parameters' . All other process parameters and responses are conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially 'mixed' , such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are described in detail and an extension is given that allows for the spatial correlation of the individual 'states' given the hyper-parameters.

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Two-stage Bayesian models—application to ZEDB project

Cited by 15 publications

References 8 publications

Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty

Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty

Bayesian updating of optimal release time for software systems

A comparison of one-stage and two-stage Bayesian processes in engineering decision-making

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