Sarah J. Dunnett

Event-tree analysis using binary decision diagrams

This paper is concerned with ETA (event-tree analysis) where the branch point event causes are defined using fault trees. Attention is on the nontrivial situation where there are dependencies amongst the branch point events. The dependencies are due to component-failures in more than one of the fault trees. In these situations the analysis methods based on traditional FTA (fault-tree analysis) are inaccurate and inefficient. The inaccuracies are not consistent across the outcome events. If frequency predictions calculated in this way are then used in a risk assessment then the relative risks would be distorted and could lead to resources being used inappropriately to reduce the overall risk. A new approach using BDD (binary decision diagram) is described which addresses these deficiencies.

Phased mission modelling of systems with maintenance-free operating periods using simulated Petri nets

A common scenario in engineering is that of a system which operates throughout several sequential and distinct periods of time, during which the modes and consequences of failure differ from one another. This type of operation is known as a phased mission, and for the mission to be a success the system must successfully operate throughout all of the phases. Examples include a rocket launch and an aeroplane flight. Component or sub-system failures may occur at any time during the mission, yet not affect the system performance until the phase in which their condition is critical. This may mean that the transition from one phase to the next is a critical event that leads to phase and mission failure, with the root cause being a component failure in a previous phase. A series of phased missions with no maintenance may be considered as a maintenance-free operating period (MFOP). This paper describes the use of a Petri net (PN) to model the reliability of the MFOP and phased missions scenario. The model uses Monte-Carlo simulation to obtain its results, and due to the modelling power of PNs, can consider complexities such as component failure rate interdependencies and mission abandonment. The model operates three different types of PN which interact to provide the overall system reliability modelling. The model is demonstrated and validated by considering two simple examples that can be solved analytically.

A mathematical theory to two-dimensional blunt body sampling

Abstract A study is made of the aspiration of small airborne dust particles into a bulky sampling head. The governing equations are solved using the Linear Boundary Integral Equation (L.B.I.E.) Method which involves an approximation of Greens Integral Formula. Results are obtained for two-dimensional cylindrical and rectangular samplers with the inlet facing the oncoming fluid. It is demonstrated that the finite size of the inlet and the shape of the sampler are very important to the fluid mechanics in the vicinity of the orifice and so it is essential that accurate flow calculations are obtained in this region. The numerical results obtained are shown to agree well with previous experimental and theoretical results but the L.B.I.E. method has many advantages over these methods in that it can easily be extended to more complex sampler shapes and to arbitrary sampling positions.

The Mathematics of Blunt Body Sampling

1 General Introduction.- 2 A Review of Past Work on Particle Sampling.- 3 A Comparison of Analytically Derived Expressions in Blunt Body Sampling with those Derived Empirically.- 4 A Boundary Integral Equation Analysis of Blunt Body Sampling in Two Dimensions.- 5 Mathematical Investigation of the Sampling Efficiency of a Two-Dimensional Blunt Sampler.- 6 The Effects of the Particle Reynolds Number on the Aspiration of Particles into a Blunt Sampler.- 7 The Aspiration of Non-Spherical Particles into a Bulky Sampling Head.- 8 An Empirical Model for the Aspiration Efficients of Blunt Aerosol Samplers Orientated at an Angle to the Oncoming Flow.- 9 Use of the Boundary Element Method for Modelling Three- Dimensional Samplers.- 10 The Human Head as a Blunt Aerosol Sampler.- 11 Conclusions.- References.

Cause–consequence analysis of non-repairable phased missions

Abstract Many systems can be modelled as a mission made up of a sequence of discrete phases. Each phase has a different requirement for successful completion and mission failure will result if any phase is unsuccessful. Fault tree analysis and Markov techniques have been used previously to model this type of system for non-repairable and repairable systems, respectively. Cause–consequence analysis is an alternative assessment technique capable of modelling all system outcomes on one logic diagram. The structure of the diagram has been shown to have advantageous features in both its representation of the system failure logic and its subsequent quantification, which could be applied to phased mission analysis. This paper outlines the use of the cause–consequence diagram method for systems undergoing non-repairable phased missions. Methods for construction of the cause–consequence diagram are first considered. The disjoint nature of the resulting diagram structure can be utilised in the later quantification process. The similarity with the Binary Decision Diagram method enables the use of efficient and accurate solution routines.

Improved Efficiency in the Analysis of Phased Mission Systems With Multiple Failure Mode Components

Systems often operate in phased missions where their reliability structure varies over a set of consecutive time periods, known as phases. The reliability of a phased mission is defined as the probability that all phases in the mission are completed without failure. While the Binary Decision Diagram (BDD) method has been shown to be the most efficient solution for measuring the reliability of phased missions with non-repairable components with mutually exclusive failure modes, the existing BDD based methods are still unable to analyze large systems without considerable computational expense. This paper introduces a new BDD based method that is shown to provide improved efficiency and accuracy in the repeat analysis of this type of phased mission.

A mathematical study of aerosol sampling by an idealised blunt sampler oriented at an angle to the wind : The role of gravity

Abstract In this paper a mathematical approach is adopted to model the flow of air and airborne particles into an idealised spherical aerosol sampler whose single circular inlet is oriented at an angle α to the undisturbed freestream. From detailed knowledge of the airflow, the paths of suspended particles in the flow were calculated and the aspiration efficiency of the sampler determined. In tracing the particle paths both inertial and gravitational forces were considered, and values of α up to 60° were investigated. The results were compared with data obtained for the same sampling system in wind tunnel studies, and were generally in good agreement. It was found that the common practise of neglecting gravity when predicting aspiration is only reasonable in certain situations, for example, for samplers facing the airflow the effects of gravity upon aspiration were found to be negligible even at low wind speeds of O(10 −1 ) m s −1 . However, as the sampler orientation to the airflow increases above zero this assumption was found to lead to increasing errors. In the case of an orientation of 60° to the airflow errors in aspiration efficiency greater than 10% were found to occur even in wind speeds as large as 6 m s −1 for the samplers considered.

A Mathematical Study of the Sampling Characteristics of a Thin-walled Sampler Operating in Calm Air

A study is made of the sampling characteristics of a thin-walled cylindrical sampler operating at various orientations in calm air. A mathematical approach is adopted to model the problem which gives an accurate description of the flow field in the vicinity of the sampling inlet. The paths of the particles in the air are then traced and the sampling efficiency investigated. In tracing the paths of the particles both inertial and gravitational effects are considered. The surface formed by the limiting particle trajectories, separating the sampled and unsampled particles, in the undisturbed flow determines the aspiration efficiency of the sampler. If the sampler is vertical, then the situation is symmetrical and the cross section of the surface formed by the limiting particle trajectories, e.g., A 0 is known to be circular. For all other orientations of the sampler the symmetry is lost, and the shape A 0 is then unknown and in this paper is investigated for various situations. The size range of particles in...

A numerical study of the sampling efficiency of a tube sampler operating in calm air facing both vertically upwards and downwards

In this paper the performance of a thin-walled sampling tube operating in calm air, pointing both vertically upwards and downwards, is investigated. The problem is considered mathematically and the sampler is modelled as a long circular cylinder. Two mathematical models have been developed to determine the flow field around the sampler, one model assumes potential flow and the other takes into account the viscous effects of the flow. From detailed knowledge of the airflow, the paths of suspended particles in the fluid flow were calculated and the aspiration efficiency of the sampler determined. The dependence of the efficiency upon the particle size and suction rate are considered for various operating conditions and a comparison made with available experimental data. The results obtained using the two different flow models are compared and hence the effects of assuming potential flow, an assumption often made when studying aerosol sampling, are investigated. It is found that neglecting the viscous effects of the fluid results in a higher predicted value of the aspiration efficiency, A. However, in all the cases considered, the difference in the values of A predicted is never large and the general behaviour of A is always the same.

The effects of finite reynolds number on the aspiration of particles into a bulky sampling head

Abstract A study is made of the aspiration of dust particles, suspended in an ideal fluid, into a bulky sampling head. The particles are assumed to be spherical and suspended without sedimentation in the fluid flowing past the sampler. The effects of the particle having a finite local Reynolds number are investigated. Numerical results are obtained for two cases, namely when the sampler is smooth and clean and the particles are solid so that no particles will adhere to the sampler and also when the sampler is sticky or the particles are liquid so that all the particles which hit the sampler adhere to it. It is found that the effects on the aspiration of particles of the increasing inertia forces are dependent upon a parameter α, the particle Reynolds number. When this parameter is in the range of its largest value m most experimental situations the results obtained are found in some circumstances to differ by over 100% from the corresponding results obtained by neglecting the finiteness of the Reynolds number.