Mount Cameroon is considered the only active volcano along a 1600 km long chain of volcanic complexes called the Cameroon Volcanic Line (CVL). It has erupted seven times during the last 100 years, the most recent was in May 2000. The approximately 500,000 inhabitants that live and work around the fertile flanks are exposed to impending threats from volcanic eruptions and earthquakes. In this thesis, a hazard assessment study that involves both statistical modelling of seismic hazard parameters and the evaluation of a future volcanic risk was undertaken on Mount Cameroon. The Gutenberg-Richter magnitude-frequency relations, the annual activity rate, the maximum magnitude, the rate of volcanic eruptions and risks assessment were examined. The seismic hazard parameters were estimated using the Maximum Likelihood Method on the basis of a procedure which combines seismic data containing incomplete files of large historical events with complete files of short periods of observations. A homogenous Poisson distribution model was applied to previous recorded volcanic eruptions of Mount Cameroon to determine the frequency of eruption and assess the probability of a future eruption. Frequency-magnitude plots indicated that Gutenberg-Richter b-values are partially dependent on the maximum regional magnitude and the method used in their calculation. b-values showed temporal and spatial variation with an average value of 1.53 ± 0.02. The intrusion of a magma body generating the occurrence of relatively small earthquakes as observed in our instrumental catalogue, could be responsible for this high anomalous b-value. An epicentre map of locally recorded earthquakes revealed that the southeastern zone is the most seismically active part of the volcano. The annual mean activity rate of the seismicity strongly depends on the time span of the seismic catalogue and results showed that on average, one earthquake event occurs every 10 days. The maximum regional magnitude values which had been determined from various approaches overlap when their standard deviations are taken into account. However, the magnitude distribution model of the Mt. Cameroon earthquakes might not follow the form of the Gutenberg-Richter frequency magnitude relationship. The datations of the last eruptive events that have occurred on Mt. Cameroon volcanic complex are presented. No specific pattern was observed on the frequency of eruptions, which means that a homogenous Poisson distribution provides a suitable model to estimate the rate of occurrence of volcanic eruptions and evaluate the risk of a future eruption. Two different approaches were used to estimate the mean eruption rate (λ) and both yielded a value of 0.074. The results showed that eruptions take place on average once every 13 years and, with the last eruption occurring over 15 years ago, it is considered that there is at present a high risk of an eruption to occur. / Dissertation (MSc)--University of Pretoria, 2016. / Geology / MSc / Unrestricted

We consider a class of periodic preventive maintenance (PM) optimization problems, for a single piece of equipment that deteriorates with time or use, and can be repaired upon failure, through corrective maintenance (CM). We develop analytical and simulation-based optimization models that seek an optimal periodic PM policy, which minimizes the sum of the expected total cost of PMs and the risk-averse cost of CMs, over a finite planning horizon. In the simulation-based models, we assume that both types of maintenance actions are imperfect, whereas our analytical models consider imperfect PMs with minimal CMs. The effectiveness of maintenance actions is modeled using age reduction factors. For a repairable unit of equipment, its virtual age, and not its calendar age, determines the associated failure rate. Therefore, two sets of parameters, one describing the effectiveness of maintenance actions, and the other that defines the underlying failure rate of a piece of equipment, are critical to our models. Under a given maintenance policy, the two sets of parameters and a virtual-age-based age-reduction model, completely define the failure process of a piece of equipment. In practice, the true failure rate, and exact quality of the maintenance actions, cannot be determined, and are often estimated from the equipment failure history. We use a Bayesian approach to parameter estimation, under which a random-walk-based Gibbs sampler provides posterior estimates for the parameters of interest. Our posterior estimates for a few datasets from the literature, are consistent with published results. Furthermore, our computational results successfully demonstrate that our Gibbs sampler is arguably the obvious choice over a general rejection sampling-based parameter estimation method, for this class of problems. We present a general simulation-based periodic PM optimization model, which uses the posterior estimates to simulate the number of operational equipment failures, under a given periodic PM policy. Optimal periodic PM policies, under the classical maximum likelihood (ML) and Bayesian estimates are obtained for a few datasets. Limitations of the ML approach are revealed for a dataset from the literature, in which the use of ML estimates of the parameters, in the maintenance optimization model, fails to capture a trivial optimal PM policy. Finally, we introduce a single-stage and a two-stage formulation of the risk-averse periodic PM optimization model, with imperfect PMs and minimal CMs. Such models apply to a class of complex equipment with many parts, operational failures of which are addressed by replacing or repairing a few parts, thereby not affecting the failure rate of the equipment under consideration. For general values of PM age reduction factors, we provide sufficient conditions to establish the convexity of the first and second moments of the number of failures, and the risk-averse expected total maintenance cost, over a finite planning horizon. For increasing Weibull rates and a general class of increasing and convex failure rates, we show that these convexity results are independent of the PM age reduction factors. In general, the optimal periodic PM policy under the single-stage model is no better than the optimal two-stage policy. But if PMs are assumed perfect, then we establish that the single-stage and the two-stage optimization models are equivalent. / text