In decision analysis, continuous uncertainties (i.e., the volume of oil in a reservoir) must be approximated by discrete distributions for use in decision trees, for example. Many methods of this process, called discretization, have been proposed and used for decades in practice. To the author’s knowledge, few studies of the methods’ accuracies exist, and were of only limited scope. This work presents a broad and systematic analysis of the accuracies of various discretization methods across large sets of distributions. The results indicate the best methods to use for approximating the moments of different types and shapes of distributions. New, more accurate, methods are also presented for a variety of distributional and practical assumptions. This first part of the work assumes perfect knowledge of the continuous distribution, which might not be the case in practice. The distributions are often elicited from subject matter experts, and because of issues such as cognitive biases, may have assessment errors. The second part of this work examines the implications of this error, and shows that differences between some discretization methods’ approximations are negligible under assessment error, whereas other methods’ errors are significantly larger than those because of imperfect assessments. The final part of this work extends the analysis of previous sections to applications to the Project Evaluation and Review Technique (PERT). The accuracies of several PERT formulae for approximating the mean and variance are analyzed, and several new formulae presented. The new formulae provide significant accuracy improvements over existing formulae. / text

In overwhelming majority of the petroleum or petrochemical plants, pressure vessels and process piping play important roles among the major elements of static equipments. So, based on the integrity of safety management for the petroleum or petrochemical plants and reduction of the operation risks, some objective schemes of the systematic failure evaluations and assessments should be established in order to optimize the resources of inspection and maintenance. However, performing the inspections based on the conventional methodologies, some uncontrolled factors which caused by the environments and inspection methods may exist and affect the assessment of the estimated corrosion rate. If the influences of the uncontrolled factors were not considered and compensated in the assessment of the estimated corrosion rate, some underestimate or unreasonable results would be obtained which lead potential risks may exist in the plants. Moreover, the measured data of some parameters, for example, operation pressure, corrosion condition, allowable stress, which were used to evaluate the estimated corrosion rate of the pressure components may exhibit a normal or non-normal distribution. Under such circumferences, if one used the nominal values of the measured parameters to assessment the safety conditions of the pressure components, potential risks may exist in the petroleum or petrochemical plants at the final stage of long-term operation. With an eye to obtain more conservative and objective assess results for pressure equipments in the long-term operation, three subjects will be differentiated between the evaluation of estimated corrosion rate, failure probability of pressure vessels and pressure safety valve (PSVs). First, based on the pressure boundaries suffered from general corrosion, a statistical methodology was proposed to modify the assessment of estimated corrosion rates for the pressure components in conventional methodology. Furthermore, the obtained results of the estimated corrosion rates will be used to assess the failure probability of pressure components based on the upper limited value. By adopting First Order Second Moment (FOSM) method, the failure probability was approached for the pressure components in long term operation. Moreover, for the sake of optimize the inspection and maintenance resources based on the acceptable risk of the plant owners, typical semi-quantitative risk based inspection (RBI) methodology to each pressure vessel are proposed in safety management based on the approached failure probability. Besides, the final protection for the pressure equipments when the pressure systems were upset - pressure safety valves (PSVs), are also play important roles to system evaluation and safety management for pressurized system. So, follow the semi-quantitative RBI methodology, the objective evaluation schemes together with the suggested inspection interval were conservatively established. Based on the conclusion of the studies, few pressure components with high failure probability will raise the operation risk of the pressurized system. It is an effective way to reduce the operation risk of the pressurized system by shift the limited resource of inspection/maintenance on the pressure components with high risk and obtain further control with effective strategies. Moreover, the conclusion also shows the prospective inspection intervals of PSVs which time-based strategy according to the local regulations (2-year based) should be change to condition-based strategy to reduce the operation risk.