Bent Natvig

TWO SUGGESTIONS OF HOW TO DEFINE A MULTISTATE COHERENT SYSTEM

One inherent weakness of traditional reliability theory is that the system and the components are always described just as functioning or failed. However, recent papers by Barlow and Wu (1978) and El-Neweihi et al. (1978) have made significant contributions to start building up a theory for a multistate system of multistate components. Here the states represent successive levels of performance ranging from a perfect functioning level down to a complete failure level. In the present paper we will give two suggestions of how to define a multistate coherent system. The first one is more general than the one introduced in the latter paper, the results of which are, however, extendable. (This is also true for a somewhat more general model than ours, treated in independent work by Griffith (1980).) Furthermore, some new definitions and results are given (which trivially extend to the latter model). Our second model is similarly more general than the one introduced in Barlow and Wu (1978), the results of which are again extendable. In fact we believe that most of the theory for the traditional binary coherent system can be extended to our second suggestion of a multistate coherent system.

A suggestion of a new measure of importance of system components

In this paper we suggest a new measure of the importance of a component in a coherent system and derive some of its properties. The measure is for the case of components not undergoing repair proportional to the expected reduction in the remaining system life-time due to the failure of the component. This measure seems to be a useful guide during the system development phase as to which components should receive the most urgent attention in order to increase the systems expected life-time. The properties of the measure are compared with the ones of a measure suggested by Barlow and Proschan [1].

Environmental risk and the precautionary principle. "Late lessons from early warnings" applied to genetically modified plants

The environmental risk associated with genetically modified organisms (GMO) implies that new approaches to risk assessment, risk management and risk communication are needed. In this paper we discuss the role of the precautionary principle in policy responses to GMO risk. We first discuss application of the criteria in the European Environment Agency report “Late lessons from early warnings: The precautionary principle 1896–2000” to environmental GMO risk, with focus on crop plants. Moreover, we discuss Bayesian analysis in the context of improving the informational basis for decision‐making under uncertainty. Finally, environmental uncertainties are intertwined with economic uncertainties. Providing incentives for improved risk assessment, risk management and risk communication is crucial for enhancing environmental and social responsibility and thereby facilitate implementation of precautionary approaches. We discuss environmental and social screening of companies as an example of how such incentives can be provided.

MULTISTATE RELIABILITY THEORY-A CASE STUDY

Fortunately traditional reliability theory, where the system and the components are always described simply as functioning or failed, is on the way to being replaced by a theory for multistate systems of multistate components. However, there is a need for several convincing case studies demonstrating the practicability of the generalizations introduced. In this paper an electrical power generation system for two nearby oilrigs will be discussed. The amounts of power that may possibly be supplied to the two oilrigs are considered as system states.

On the reduction in remaining system lifetime due to the failure of a specific component

In a previous paper, Natvig [4], we suggested a new measure of the importance of a component in a coherent system and derived some of its properties. The measure is for the case of components not undergoing repair proportional to the expected reduction in remaining system lifetime due to the failure of the component. In the present paper, we arrive at the whole distribution of this reduction in remaining system lifetime. Furthermore, for the case where components have proportional hazards, and are not repaired, a speculation of another measure is given. This measure is proportional to the derivative of the expected total lifetime of a new system with respect to the inverse of the components proportional hazard rate.

A Bayesian hierarchical spatio-temporal model for significant wave height in the North Atlantic

Bad weather and rough seas continue to be a major cause for ship losses and is thus a significant contributor to the risk to maritime transportation. This stresses the importance of taking severe sea state conditions adequately into account in ship design and operation. Hence, there is a need for appropriate stochastic models describing the variability of sea states, taking into account long-term trends related to climate change. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without considering spatial variations. As far as the authors are aware, no model of significant wave height to date exploits the flexible framework of Bayesian hierarchical space-time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet at the same time remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space-time model for significant wave height. The model has been fitted by significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to monthly and daily data will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data will be presented.

A review and Bayesian meta-analysis of clinical efficacy and adverse effects of 4 atypical neuroleptic drugs compared with haloperidol and placebo.

Aims: The objective of the study was to examine the efficacy and the degree of adverse effects connected with atypical neuroleptic drugs and haloperidol by using a previously described Bayesian statistical method that includes both direct and indirect comparisons simultaneously. Methods: The authors used the results of 30 double-blind, randomized studies including comparisons of 4 atypical neuroleptics and haloperidol, head-to-head or against placebo. We calculated the response ratios for drugs against placebo and thereafter the relative response ratios for one drug against another. With uniform priors, we calculated and ranked the posterior estimates of response ratios for antipsychotic effect, weight gain, and occurrence of extrapyramidal symptoms. Results: All second-generation neuroleptics analyzed are fairly effective with response ratios against placebo ranging between 1.55 (credibility interval, 1.36-1.76) and 1.99 (1.76-2.26), with clozapine being the most effective and aripiprazole the least effective among them. The risk of inducing weight gain is clearly very high for all 5 neuroleptic drugs compared with placebo with response ratios of 12.21 (10.22-15.05) for olanzapine and 11.28 (6.89-17.77) for clozapine. There is a clear increased risk of extrapyramidal adverse effects for haloperidol compared with placebo as the response ratio is 2.33 (2.03-2.49). The other drugs all have considerably less risk of extrapyramidal adverse effects. Conclusions: The 4 second-generation neuroleptics included in our meta-analysis show only small differences in overall efficacy, with clozapine being the most effective and aripiprazole the least effective among them. When the risk of adverse effects is analyzed, olanzapine and clozapine are afflicted with the highest risk of inducing weight gain and haloperidol with extrapyramidal symptoms. Even aripiprazole and risperidone, however, induce considerable weight gain compared with placebo but may be acceptable alternatives when tailoring drug treatment to the individual patient.

Improved upper bounds for the availabilities in a fixed time interval for multistate monotone systems

In this paper upper and lower bounds for the availability and unavailability, to any level, in a fixed time interval are arrived at for multistate monotone systems based on corresponding information on the multistate components. These are assumed to be maintained and interdependent. Such bounds are of great interest when trying to predict the performance process of the system, noting that exact expressions are obtainable just for trivial systems. The bounds given generalize the existing bounds known in traditional binary theory, and represent improvements of the ones now being developed in multistate theory.

Possibility versus probability

The main objective of this note is to try to indicate that a possibility distribution at least in some applications can be interpreted as a family of probabilities (possibly subjective). An advantage of the latter interpretation is that subsequent derivations can be made by well proven probabilistic arguments rather than relying on an intuition concerning the properties of possibility distributions which is not well developed. Multistate reliability theory is given as an example of an area of application where the probabilistic approach seems far superior.

Modelling ocean wave climate with a Bayesian hierarchical space–time model and a log-transform of the data

Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.