Reliability analysis for hazard and operability studies

Fault tree analysis is used as a tool within hazard and operability (Hazop) studies. The present study proposes a new methodology for obtaining the exact TOP event probability of coherent fault trees. The technique uses a top-down approach similar to that of FATRAM. This new Fault Tree Disjoint Reduction Algorithm resolves all the intermediate events in the tree except OR gates with basic event inputs so that a near minimal cut sets expression is obtained. Then Bennetts' disjoint technique is applied and remaining OR gates are resolved. The technique has been found to be appropriate as an alternative to Monte Carlo simulation methods when rare events are countered and exact results are needed. The algorithm has been developed in FORTRAN 77 on the Perq workstation as an addition to the Aston Hazop package. The Perq graphical environment enabled a friendly user interface to be created. The total package takes as its input cause and symptom equations using Lihou's form of coding and produces both drawings of fault trees and the Boolean sum of products expression into which reliability data can be substituted directly.

The economic impact of high growth start-ups:understanding the challenge for policy in the UK

Objectives The creation of more high-growth firms continues to be a key component of enterprise policy throughout the countries of the OECD. In the UK the developing enterprise policy framework highlights the importance of supporting businesses with growth potential. The difficulty, of course, is the ability of those delivering business support policies to accurately identify those businesses, especially at start-up, which will benefit from interventions and experiences an enhanced growth performance. This paper has a core objective of presenting new data on the number of high growth firms in the UK and providing an assessment of their economic significance. Approach This paper uses a specially created longitudinal firm-level database based on the Inter-Departmental Business Register (IDBR) held by the Office of National Statistics (ONS) for all private sector businesses in the UK for the period 1997-2008 to investigate the share of high-growth firms (including a sub-set of start-up more commonly referred to as gazelles) in successive cohorts of start-ups. We apply OECD definitions of high growth and gazelles to this database and are able to quantify for the first time their number (disaggregated by sector, region, size) and importance (employment and sales). Prior Work However, what is lacking at the core of this policy focus is any comprehensive statistical analysis of the scale and nature of high-growth firms in cohorts of new and established businesses. The evidence base in response to the question “Why do high-growth firms matter?” is surprisingly weak. Important work in this area has been initiated by Bartelsman et al., (2003),Hoffman and Jünge (2006) and Henreksen and Johansson (2009) but to date work in the UK has been limited (BERR, 2008b). Results We report that there are ~11,500 high growth firms in the UK in both 2005 and 2008. The share of high growth start-ups in the UK in 2005 (6.3%) was, contrary to the widely held perception in policy circles, higher than in the United States (5.2%). Of particular interest in the analysis are the growth trajectories (pattern of growth) of these firms as well as the extent to which they are restricted to technology-based or knowledge-based sectors. Implications and Value Using hitherto unused population data for the first time we have answered a fundamental research and policy question on the number and scale of high growth firms in the UK. We draw the conclusion that this ‘rare’ event does not readily lend itself to policy intervention on the grounds that the significant effort needed to identify such businesses ex ante would appear unjustified even if it was possible.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.