Risk Assessment and Safety Evaluation Using Probabilistic Fault Tree Analysis

Risk assessment is an essential prelude to the development of accident prevention strategies in any chemical or petrochemical industry. Many techniques and methodologies such as HAZOP, failure mode effect analysis, fault tree analysis, preliminary hazard analysis, quantitative risk assessment and probabilistic safety analysis are available to conduct qualitative, quantitative, and probabilistic risk assessment. However, these methodologies are limited by: extensive data requirements, the length of study, results are not directly interpretable for decision making, simulation is often difficult, and they are applicable only at the operation or late design stage. Khan et al. (2001a) recently proposed a detailed methodology for risk assessment and safety evaluation. This methodology is simple, yet it is effective in safety and design-related decision making, and it has been applied successfully to many case studies. It is named SCAP, where S stands for safety, C and A stand for credible accident respectively, and P stands for probabilistic fault tree analysis. This paper recapitulates the SCAP methodology and demonstrates its application to a petrochemical plant.     

Mortality risk increases with natal dispersal distance in American martens

The assumption that mortality risk increases with dispersal distance has rarely been tested. We compared patterns of natal dispersal in the American marten (Martes americana) between a large regenerating forest landscape and an uncut landscape that was dominated by more mature forest to test whether mortality risk increased with dispersal distance, and whether variation in mortality risk influenced dispersal distance. Mortality risk increased with dispersal distance in both landscape treatments, but the distance-dependent increase in mortality in the regenerating landscape was twice that in the uncut landscape. Differences in body condition, supported by other data on foraging efficiency, suggested that juveniles from the regenerating landscape were less able to cope with the energetic demands of dispersal compared with juveniles from older forests. Juveniles travelled shorter distances in the regenerating versus uncut landscape. These results implied that dispersal was costly in terms of juvenile survival and that mean dispersal distance was shaped, in part, by mortality risk.     

The Wald Statistic in Proportional Hazards Hypothesis Testing

In survivorship modelling using the proportional hazards model of Cox (1972, Journal of the Royal Statistical Society, Series B, 34, 187–220), it is often desired to test a subset of the vector of unknown regression parameters β in the expression for the hazard rate at time t. The likelihood ratio test statistic is well behaved in most situations but may be expensive to calculate. The Wald (1943, Transactions of the American Mathematical Society 54, 426–482) test statistic is easier to calculate, but has some drawbacks. In testing a single parameter in a binomial logit model, Hauck and Donner (1977, Journal of the American Statistical Association 72, 851–853) show that the Wald statistic decreases to zero the further the parameter estimate is from the null and that the asymptotic power of the test decreases to the significance level. The Wald statistic is extensively used in statistical software packages for survivorship modelling and it is therefore important to understand its behavior. The present work examines empirically the behavior of the Wald statistic under various departures from the null hypothesis and under the presence of Type I censoring and covariates in the model. It is shown via examples that the Wald statistic's behavior is not as aberrant as found for the logistic model. For the single parameter case, the asymptotic non-null distribution of the Wald statistic is examined.