J. René van Dorp

The Standard Two-Sided Power Distribution and its Properties: With Applications in Financial Engineering

This article discusses a family of distributions which would seem not to receive proper attention in the literature. The two-parameter distribution is introduced with an application in the financial engineering domain. Special cases of this family include the triangular distribution, the standard power function distribution, and the uniform distribution. Properties of the distribution are investigated and the maximum likelihood estimation procedure for its two parameters is derived. The flexibility of the family as compared to that of the beta family is discussed.

A traffic density analysis of proposed ferry service expansion in San Francisco Bay using a maritime simulation model

Abstract A proposal has been made to the California legislature to dramatically increase the frequency and coverage of ferry service in the San Francisco Bay area. A major question in the approval process is the effect of this expansion on the level of congestion on the waterway and the effect this will have on the safety of vessels in the area. A simulation model was created to estimate the number of vessel interactions in the current system and their increases caused by three alternative expansion plans. The output of the simulation model is a geographic profile showing the frequency of vessel interactions across the study area, thus representing the level of congestion under each alternative. Comparing these geographic interaction profiles to a similar one generated for the current ferry service in the San Francisco Bay allows evaluation of the increase in exposure of ferries to adverse conditions, such as, for example, the interaction of high-speed ferries in restricted visibility conditions. This analysis has been submitted to the legislature as part of the overall assessment of the proposal and will be used in the expansion decision.

A Bayes approach to step-stress accelerated life testing

This paper develops a Bayes model for step-stress accelerated life testing. The failure times at each stress level are exponentially distributed, but strict adherence to a time-transformation function is not required. Rather, prior information is used to define indirectly a multivariate prior distribution for the failure rates at the various stress levels. Our prior distribution preserves the natural ordering of the failure rates in both the prior and posterior estimates. Methods are developed for Bayes point estimates as well as for making probability statements for use-stress life parameters. The approach is illustrated with an example.

The Prince William Sound Risk Assessment

After the grounding of the Exxon Valdez and its subsequent oil spill, all parties with interests in Prince William Sound (PWS) were eager to prevent another major pollution event. While they implemented several measures to reduce the risk of an oil spill, the stakeholders disagreed about the effectiveness of these measures and the potential effectiveness of further proposed measures. They formed a steering committee to represent all the major stakeholders in the oil industry, in the government, in local industry, and among the local citizens. The steering committee hired a consultant team, which created a detailed model of the PWS system, integrating system simulation, data analysis, and expert judgment. The model was capable of assessing the current risk of accidents involving oil tankers operating in the PWS and of evaluating measures aimed at reducing this risk. The risk model showed that actions taken prior to the study had reduced the risk of oil spill by 75 percent, and it identified measures estimated to reduce the accident frequency by an additional 68 percent, including improving the safety-management systems of the oil companies and stationing an enhanced-capability tug, called the Gulf Service, at Hinchinbrook Entrance. In all, various stakeholders made multimillion dollar investments to reduce the risk of further oil spills based on the results of the risk assessment.

Speaking the Truth in Maritime Risk Assessment

Several major risk studies have been performed in recent years in the maritime transportation domain. These studies have had significant impact on management practices in the industry. The first, the Prince William Sound risk assessment, was reviewed by the National Research Council and found to be promising but incomplete, as the uncertainty in its results was not assessed. The difficulty in assessing this uncertainty is the different techniques that need to be used to model risk in this dynamic and data-scarce application area. In previous articles, we have developed the two pieces of methodology necessary to assess uncertainty in maritime risk assessment, a Bayesian simulation of the occurrence of situations with accident potential and a Bayesian multivariate regression analysis of the relationship between factors describing these situations and expert judgments of accident risk. In this article, we combine the methods to perform a full-scale assessment of risk and uncertainty for two case studies. The first is an assessment of the effects of proposed ferry service expansions in San Francisco Bay. The second is an assessment of risk for the Washington State Ferries, the largest ferry system in the United States.

On a risk management analysis of oil spill risk using maritime transportation system simulation

Is it safer for New Orleans river gambling boats to be underway than to be dockside? Is oil transportation risk reduced by lowering wind restrictions from 45 to 35 knots at Hinchinbrook Entrance for laden oil tankers departing Valdez, Alaska? Should the International Safety Management (ISM) code be implemented fleet-wide for the Washington State Ferries in Seattle, or does it make more sense to invest in additional life craft? Can ferry service in San Francisco Bay be expanded in a safe manner to relieve high way congestion? These risk management questions were raised in a series of projects spanning a time frame of more than 10 years. They were addressed using a risk management analysis methodology developed over these years by a consortium of universities. In this paper we shall briefly review this methodology which integrates simulation of Maritime Transportation Systems (MTS) with incident/accident data collection, expert judgment elicitation and a consequence model. We shall describe recent advances with respect to this methodology in more detail. These improvements were made in the context of a two-year oil transportation risk study conducted from 2006–2008 in the Puget Sound and surrounding waters. An application of this methodology shall be presented comparing the risk reduction effectiveness analysis of a one-way zone, an escorting and a double hull requirement in the same context.

A general Bayes exponential inference model for accelerated life testing

This article develops a general Bayes inference model for accelerated life testing assuming failure times at each stress level are exponentially distributed. Using the approach, Bayes point estimates as well as probability statements for use-stress life parameters may be inferred from the following testing scenarios: regular life testing, fixed-stress testing, step-stress testing, profile-stress testing, and also mixtures thereof. The inference procedure uses the well known Markov chain Monte Carlo (MCMC) methods to derive posterior quantities and accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The approach is illustrated with an example.

A Bayesian paired comparison approach for relative accident probability assessment with covariate information

One of the challenges managers face when trying to understand complex, technological systems (in their efforts to mitigate system risks) is the quantification of accident probability, particularly in the case of rare events. Once this risk information has been quantified, managers and decision makers can use it to develop appropriate policies, design projects, and/or allocate resources that will mitigate risk. However, rare event risk information inherently suffers from a sparseness of accident data. Therefore, expert judgment is often elicited to develop frequency data for these high-consequence rare events. When applied appropriately, expert judgment can serve as an important (and, at times, the only) source of risk information. This paper presents a Bayesian methodology for assessing relative accident probabilities and their uncertainty using paired comparison to elicit expert judgments. The approach is illustrated using expert judgment data elicited for a risk study of the largest passenger ferry system in the US.

A general Bayes weibull inference model for accelerated life testing

This article presents the development of a general Bayes inference model for accelerated life testing. The failure times at a constant stress level are assumed to belong to a Weibull distribution, but the specification of strict adherence to a parametric time-transformation function is not required. Rather, prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels and the common shape parameter. Using the approach, Bayes point estimates as well as probability statements for use-stress (and accelerated) life parameters may be inferred from a host of testing scenarios. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known MCMC (Markov Chain Monte Carlo) methods to derive posterior approximations. The approach is illustrated with an example.

Generalizations of Two Sided Power Distributions and Their Convolution

Abstract A general form of a family of bounded two-sided continuous distributions is introduced. The uniform and triangular distributions are possibly the simplest and best known members of this family. We also describe families of continuous distribution on a bounded interval generated by convolutions of these two-sided distributions. Examples of various forms of convolutions of triangular distributions are presented and analyzed.