The Bayes linear approach to inference and decision-making for a reliability programme

In reliability modelling it is conventional to build sophisticated models of the probabilistic behaviour of the component lifetimes in a system in order to deduce information about the probabilistic behaviour of the system lifetime. Decision modelling of the reliability programme requires a priori, therefore, an even more sophisticated set of models in order to capture the evidence the decision maker believes may be obtained from different types of data acquisition.Bayes linear analysis is a methodology that uses expectation rather than probability as the fundamental expression of uncertainty. By working only with expected values, a simpler level of modelling is needed as compared to full probability models.In this paper we shall consider the Bayes linear approach to the estimation of a mean time to failure MTTF of a component. The model built will take account of the variance in our estimate of the MTTF, based on a variety of sources of information.     

Comparison of empirical Bayes and full Bayes approaches for before-after road safety evaluations

The empirical Bayes (EB) approach has now gained wide acceptance among researchers as the much preferred one for the before-after evaluation of road safety treatments. In this approach, the before period crash experience at treated sites is used in conjunction with a crash prediction model for untreated reference sites to estimate the expected number of crashes that would have occurred without treatment. This estimate is compared to the count of crashes observed after treatment to evaluate the effect of the treatment. This procedure accounts for regression-to-the-mean effects that result from the natural tendency to select for treatment those sites with high observed crash frequencies. Of late, a fully Bayesian (FB) approach has been suggested as a useful, though complex alternative to the empirical Bayes approach in that it is believed to require less data for untreated reference sites, it better accounts for uncertainty in data used, and it provides more detailed causal inferences and more flexibility in selecting crash count distributions. This paper adds to the literature on comparing the two Bayesian approaches through empirical applications. The main application is an evaluation of the conversion of road segments from a four-lane to a three-lane cross-section with two-way left-turn lanes (also known as road diets). For completeness, the paper also summarizes the results of an earlier application pertaining to the evaluation of conversion of rural intersections from unsignalized to signalized control. For both applications, the estimated safety effects from the two approaches are comparable.     

Investigating the effects of the fixed and varying dispersion parameters of Poisson-gamma models on empirical Bayes estimates

Traditionally, transportation safety analysts have used the empirical Bayes (EB) method to improve the estimate of the long-term mean of individual sites; to correct for the regression-to-the-mean (RTM) bias in before-after studies; and to identify hotspots or high risk locations. The EB method combines two different sources of information: (1) the expected number of crashes estimated via crash prediction models, and (2) the observed number of crashes at individual sites. Crash prediction models have traditionally been estimated using a negative binomial (NB) (or Poisson-gamma) modeling framework due to the over-dispersion commonly found in crash data. A weight factor is used to assign the relative influence of each source of information on the EB estimate. This factor is estimated using the mean and variance functions of the NB model. With recent trends that illustrated the dispersion parameter to be dependent upon the covariates of NB models, especially for traffic flow-only models, as well as varying as a function of different time-periods, there is a need to determine how these models may affect EB estimates. The objectives of this study are to examine how commonly used functional forms as well as fixed and time-varying dispersion parameters affect the EB estimates. To accomplish the study objectives, several traffic flow-only crash prediction models were estimated using a sample of rural three-legged intersections located in California. Two types of aggregated and time-specific models were produced: (1) the traditional NB model with a fixed dispersion parameter and (2) the generalized NB model (GNB) with a time-varying dispersion parameter, which is also dependent upon the covariates of the model. Several statistical methods were used to compare the fitting performance of the various functional forms. The results of the study show that the selection of the functional form of NB models has an important effect on EB estimates both in terms of estimated values, weight factors, and dispersion parameters. Time-specific models with a varying dispersion parameter provide better statistical performance in terms of goodness-of-fit (GOF) than aggregated multi-year models. Furthermore, the identification of hazardous sites, using the EB method, can be significantly affected when a GNB model with a time-varying dispersion parameter is used. Thus, erroneously selecting a functional form may lead to select the wrong sites for treatment. The study concludes that transportation safety analysts should not automatically use an existing functional form for modeling motor vehicle crashes without conducting rigorous analyses to estimate the most appropriate functional form linking crashes with traffic flow.     

Integrating RAMS engineering and management with the safety life cycle of IEC 61508

This article outlines a new approach to reliability, availability, maintainability, and safety (RAMS) engineering and management. The new approach covers all phases of the new product development process and is aimed at producers of complex products like safety instrumented systems (SIS). The article discusses main RAMS requirements to a SIS and presents these requirements in a holistic perspective. The approach is based on a new life cycle model for product development and integrates this model into the safety life cycle of IEC 61508. A high integrity pressure protection system (HIPPS) for an offshore oil and gas application is used to illustrate the approach.     

Pro/Engineer的参数化零件二次开发研究与实现

本文详细研究了利用Pro／E二次开发工具Pro／Toolkit进行参数化二次开发、原理、方法和实现的关键技术，建立了参数化零件二次开发模型和开发流程，利用VC ，实现了3D零件模型的二次开发。     

Generic probabilistic safety analysis: application to the comparison of the emergency feedwater system designs of three PWRs and to the modernisation and backfitting of older Swedish NPPs

The relationship between configuration characteristics of safety systems and their unavailabilities was examined on the basis of the results of 25 PSAs for PWR and BWR plants [1 and 2]. The results of the evaluations provide groupings of configuration characteristics and associated ranges of unavailabilities that can be expected for the various groups. The safety functions

• residual heat removal at BWR plants

• coolant make-up at BWR plants

• auxiliary/emergency feedwater supply to steam generators at PWR plants

• emergency core cooling, including containment spray injection/recirculation, at PWR plants

were considered.Two applications are reported:

• evidence of validation of the generic approach, based on the results of a blind prediction of the unavailability of the emergency feedwater function at the plants N4, Sizewell-B and Konvoi, and subsequent comparison with results obtained by conventional reliability analysis;

• outline of the use of the approach in the framework of the modernisation and backfitting programme for Swedish nuclear power plants.

In the early discussions of safety objectives for the modernisation programme, the generic approach provided input to the exploration of possible target values for safety systems. In the process of reviewing proposed technical solutions, Swedish Nuclear Power Inspectorate (SKI) is using the generic approach as one of the tools for assessing safety function unavailabilities.     

On the relationship of the cumulative jump model for random fatigue to empirical data

The cumulative jump model, consisting of a random sum of random increments, has previously been proposed, in a general format, to model the fatigue crack growth process. In this paper the cumulative jump process for random fatigue is used to model the constant-load amplitude Virkler fatigue crack growth data. It is shown, through the proper choice of the intensity function of the underlying birth process, that the mean crack growth behavior of the model may be specified to match any desired functional form. This assures reasonable agreement with experiments. For fatigue crack growth the intensity function is characterized by a constant and a random variable (this makes the underlying birth process a so-called doubly stochastic counting process). For the case of the ‘simplified' jump model (constant elementary crack increments), the constant and the random variable characterizing the intensity function may be estimated by matching approximate formulae for the mean and the variance of the model with the data. Simulations of the jump model show trajectories which behave qualitatively like the data and yield distribution functions for the crack length which match well the data.     

A comparative study of Vitamin E TPGS/HPMC supersaturated system and other solubilizer/polymer combinations to enhance the permeability of a poorly soluble drug through the skin

In transdermal drug delivery systems (TDDS), it is a challenge to achieve stable and prolonged high permeation rates across skin, because the concentration of the drug dissolved in the matrix has to be high in order to maintain zero order release kinetics of the drug. In case of poorly soluble drugs, due to thermodynamic challenges, there is a high tendency for the drug to nucleate immediately after formulating or even during storage. The present study focuses on the efficiency of vitamin E TPGS/HPMC supersaturated solution and other solubilizer/polymer systems to improve the solubility of the drug and inhibit crystal growth in the transdermal formulation. Effect of several solubilizers, for example, Pluronic F-127, vitamin E TPGS and co-solvent, for example, propylene glycol (PG) were studied on the supersaturated systems of ibuprofen as model drug. Various stabilizers such as hydroxylpropyl methylcellulose (HPMC 3 cps) and polyvinylpyrrolidone (PVP K-30) were examined to evaluate their crystal inhibitory effects. Different analytical tools were used in this study to detect the growth of crystals in the systems. Vitamin E TPGS and HPMC 3 cps formulation produced the highest permeation rate of the drug as compared to other systems. In addition, the onset of crystallization time was shown to be longer with this formulation as compared to other solubilizer/polymer combinations.