Construction and Verification of Performance and Reliability Models

Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area. Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models

On stochastic properties between some ordered random variables

A great number of articles have dealt with stochastic comparisons of ordered random variables in the last decades. In particular, distributional and stochastic properties of ordinary order statistics have been studied extensively in the literature. Sequential order statistics are proposed as an extension of ordinary order statistics. Since sequential order statistics models unify various models of ordered random variables, it is interesting to study their distributional and stochastic properties. In this work, we consider the problem of comparing sequential order statistics according to magnitude and location orders.Stochastic orderings, Reliability, Order statistics

Cost-benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with 'unreliability' is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost-benefit analysis during product development are discussed and illustrated through a simple case

Regulatory Tailoring, Reliability, and Price Volatility with Stochastic Breakdowns

Although real-world energy supply systems are subject to stochastic failures, the impacts of proposed regulations affecting these systems have typically been evaluated using non-stochastic models. This paper develops an energy market model that explicitly allows for stochastic failures and demonstrates they play an important, or even dominant, role in determining the market impacts of environmental regulations that tailor product specifications to address local or regional conditions, such as fuel-formulation requirements specific to certain regional markets within the United States. While traditional non-stochastic analyses view the tailoring of regulatory requirements by location as an efficiency-enhancing alternative to a "one size fits all" regulatory approach, they fail to consider the adverse impact on reliability in all market segments resulting from the loss of product fungibility due to tailoring. We show that regulatory impact estimates developed without explicit consideration of reliability considerations may be highly inaccurate.reliability, boutique fuels, gasoline price spikes, stochastic failures, environmental regulation, tailored regulation

Data assimilation in slow-fast systems using homogenized climate models

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization model is derived for the slow dynamics. The reliability of this reduced climate model in reproducing the statistics of the slow dynamics of the full deterministic model for finite values of the time scale separation is numerically established. The statistics however is sensitive to uncertainties in the parameters of the stochastic model. It is investigated whether the stochastic climate model can be beneficial as a forecast model in an ensemble data assimilation setting, in particular in the realistic setting when observations are only available for the slow variables. The main result is that reduced stochastic models can indeed improve the analysis skill, when used as forecast models instead of the perfect full deterministic model. The stochastic climate model is far superior at detecting transitions between regimes. The observation intervals for which skill improvement can be obtained are related to the characteristic time scales involved. The reason why stochastic climate models are capable of producing superior skill in an ensemble setting is due to the finite ensemble size; ensembles obtained from the perfect deterministic forecast model lacks sufficient spread even for moderate ensemble sizes. Stochastic climate models provide a natural way to provide sufficient ensemble spread to detect transitions between regimes. This is corroborated with numerical simulations. The conclusion is that stochastic parametrizations are attractive for data assimilation despite their sensitivity to uncertainties in the parameters.Comment: Accepted for publication in Journal of the Atmospheric Science

Separability in Stochastic Binary Systems

A Stochastic Binary System (SBS) is a mathematical model of multi-component on-off systems subject to random failures. SBS models extend classical network reliability models (where the components subject to failure are nodes or links of a graph) and are able to represent more complex interactions between the states of the individual components and the operation of the system under study. The reliability evaluation of stochastic binary systems belongs to the class of NP-Hard computational problems. Furthermore, the number of states is exponential with respect to the size of the system (measured in the number of components). As a consequence, the representation of an SBS becomes a key element in order to develop exact and/or approximation methods for reliability evaluation. The contributions of this paper are three-fold. First, we present the concept of separable stochastic binary systems, showing key properties, such as an efficient representation and complexity in the reliability evaluation. Second, we fully characterize separable systems in two ways, using a geometrical interpretation and minimum-cost operational subsystems. Finally, we show the application of separable systems in network reliability models, specifically in the all-terminal reliability model, which has a wide spectrum of applications. Index Terms—Stochastic Binary System, Network Reliability, Computational Complexity, Chernoff Inequality

Reliability assessment of cutting tool life based on surrogate approximation methods

A novel reliability estimation approach to the cutting tools based on advanced approximation methods is proposed. Methods such as the stochastic response surface and surrogate modeling are tested, starting from a few sample points obtained through fundamental experiments and extending them to models able to estimate the tool wear as a function of the key process parameters. Subsequently, different reliability analysis methods are employed such as Monte Carlo simulations and first- and second-order reliability methods. In the present study, these reliability analysis methods are assessed for estimating the reliability of cutting tools. The results show that the proposed method is an efficient method for assessing the reliability of the cutting tool based on the minimum number of experimental results. Experimental verification for the case of high-speed turning confirms the findings of the present study for cutting tools under flank wear

On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation

A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naively suspected and, in general, only breaks down at the very end of inflation.Comment: 7 pages, 3 figure