J. René van Dorp

• Doctor of Science Operations Research
• Professor (Full) at George Washington University

A general three-point elicitation model is proposed for eliciting distributions from experts. Specifically, lower and upper quantile estimates and a most likely estimate in between these quantile estimates are to be elicited, which uniquely determine a member in a flexible family of distributions that is consistent with these estimates. Multiple ex...

This research analyzes cost account-level detail from ten similar satellite programs to assess the relationship between cost and schedule variances. A model is defined to break activity into two types: level of effort (LOE), in which cost is directly proportional to the cost account’s duration and discrete, where the cost is independent of the sche...

The construction of a continuous family of distributions on a compact (bounded) set is demonstrated by concatenating, in a continuous manner, three probability density functions with bound- ed support using a modified mixture technique. The construction technique is similar to that of generalized trapezoidal (GT) distributions, but contrary to GT d...

The idea of transforming one random variate to another with a more convenient density has been developed in the first half of the 20th century. In his thesis, Norman L. Johnson (1917 – 2004) developed a pioneering system of transformations of the standard normal distribution which gained substantial popularity in the second half of the 20th century...

The Program Evaluation and Review Technique (PERT) dates back to 1959. This method evaluates the uncertainty distribution of a project’s completion time given the uncertain completion times of the activities/tasks comprised within it. Each activity’s uncertainty was defined originally by a unique two parameter beta PERT distribution satisfying what...

In this paper,we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data s...

The introduction of the Program Evaluation and Review Technique (PERT) dates back to the 1960s and has found wide application since then in the planning of construction projects. Difficulties with the interpretation of the parameters of the beta distribution let Malcolm et al. (Malcolm, D.G., et al., 1959. Application of a technique for research an...

Targeted malicious emails to enable computer network exploitation have become more insidious and more widely documented in recent years. Beyond spam or phishing designed to trick users into revealing personal information, targeted malicious email (TME) facilitates computer network exploitation and the gathering of sensitive information from targete...

In many practical problems, it is important to consider different distributions that could be used to model a data set. In this work, we analyze the generalized trapezoidal (GT) model in financial application. The primary reason for this is that the family of the GT distributions includes models with bounded domain used in risk analysis, and it bel...

A prevalence of heavy-tailed, peaked and skewed uncertainty phenomena have been cited in literature dealing with economic, physics, and engineering data. This fact has invigorated the search for continuous distributions of this nature. In this paper we shall generalize the two-sided framework presented in Kotz and van Dorp (Beyond beta: other conti...

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 Fe...

In this paper we have developed an oil outflow model for collision and grounding accidents of tankers. The collision model explicitly links input variables such as tanker hull design (single or double), displacement and speed, striking vessel displacement and speed, and the interaction angle of both vessels to output variables: longitudinal and tra...

Difficulties with the interpretation of the parameters of the beta distribution let Malcolm et al. (1959) to suggest in the Program Evaluation and Review Technique (PERT) their by now classical expressions for the mean and variance for activity completion for practical applications. In this note, we shall provide an alternative for the PERT varianc...

Preventive maintenance of mechanical equipment subject to random failures requires a lifetime distribution to establish an optimal maintenance interval. Typically, the optimal maintenance interval under an age replacement regimen is obtained by minimising the long term average cost of the maintenance activity. Only when the cost of maintaining the...

This paper presents research conducted in modeling specific exposure metrics of communities in the vicinity of public use, nontowered airports to aviation accidents that result in crash sites outside the immediate confines of a runway (termed external airport risk). Two exposure metrics are explored: a relative exposure (termed crash hazard), defin...

Maximum entropy copulae introduced by Bedford and Meeuwissen (1997) provide normative experts the option of making minimally informative assumptions given a degree of dependence constraint between two random variables. Unfortunately, their distributions functions are not available in a closed form and application requires the use of numerical metho...

The introduction of the Project Evaluation and Review Technique (PERT) dates back to the 1960's and has found wide application since then in the planning of construction projects. Difficulties with the interpretation of the parameters of the beta distribution let Malcolm et al. [1] to suggest the classical expressions for the PERT mean and variance...

The generalized standard two-sided power (GTSP) distribution was mentioned only in passing by Kotz and van Dorp Beyond Beta, Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Press, Singapore, 2004. In this paper, we shall further investigate this three-parameter distribution by presenting some novel...

Over 50 years ago, in a 1955 issue of JASA, a paper on a bounded continuous distribution by Topp and Leone [C.W. Topp and F.C. Leone, A family of J-shaped frequency functions, J. Am. Stat. Assoc. 50(269) (1955), pp. 209-219] appeared (the subject was dormant for over 40 years but recently the family was resurrected). Here, we shall investigate the...

4 Abstract: Recent advances in computation technology for decision/simulation and uncertainty analyses have revived interest in the the triangular distribution and its use to describe uncertainty of bounded input phenomena. The trapezoidal distribution, explicitly suggested by Pouliquen (1970) in the framework of risk and uncertainty analysis, is a...

In this paper we propose a four-parameter doubly-Pareto uniform (DPU) asymmetric distribution with support () whose density and cumulative distribution functions are  ∞ß ∞ constructed by seamlessly concatenating the left and right Pareto tails with a uniform central part. Properties of the distribution are described and a maximum likelihood estima...

In this paper we present a novel four parameter continuous univariate distribution that can be motivated from at least two approaches. The first one views the distribution as a generalization of the uniform one that allows for uncertainty specification at the vicinity of its bounds (gradually) represented via two Pareto tails. The second one is tha...

Recent advances in computation technology for simulation/uncertainty analyses have shed new light on the triangular distribution and its use to describe the uncertainty of bounded input phenomena. Herein, we develop a novel fitting procedure for a continuous unimodal (four-parameter) family of distributions on a bounded domain, utilizing three prop...

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 it...

Accelerated life testing (ALT) is the set of procedures used to reduce the time needed to obtain information related to life characteristics of an item, material or part of interest. Herein we focus on the comparison of different ALT designs (fixed stress, profile ALT, progressive step-stress ALT and regressive ALT) within a single Bayesian inferen...

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, desi...

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 it...

We present a two parameter family of continuous distribution on a bounded domain which has an elevated but finite density value at its lower bound. Such a characteristic appears to be useful, for example, when representing income distributions at lower income ranges. The family generalizes the one parameter Topp and Leone distribution originated in...

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 d...

Recent work in the assessment of risk in maritime transportation systems has used simulation-based probabilistic risk assessment techniques. In the Prince William Sound and Washington State Ferries risk assessments, the studies' recommendations were backed up by estimates of their impact made using such techniques and all recommendations were imple...

We develop a Bayesian multivariate analysis of expert judgment elicited using an extended form of pair-wise comparisons. The method can be used to estimate the effect of multiple factors on the probability of an event and can be applied in risk analysis and other decision problems. The analysis provides variance predictions of the quantity of inter...

Motivated by our investigations of refinements of the project evaluation and review technique (PERT), we have developed a reparameterization of the asymmetric Laplace distribution and found it to be a useful tool for extending and improving various three-point approximations of continuous distributions (pioneered by Pearson and Tukey (Biometrika 52...

A model for building statistical dependence between marginal distribution with bounded support is discussed. The model is geared towards elicitation of dependence parameters through expert judgment. The resulting joint distribution may be useful in uncertainty analyses where dependence between random variables with a bounded support is present due...

The aim of this study is to review the evolution of geothermal energy project evaluation techniques. Both power generation and heating (excluding heat pumps) projects and their evaluation techniques are reviewed. Although geothermal power generation projects have more extensive literature than the direct use applications in terms of project evaluat...

In this paper we propose and analyze a bounded density function with a jump discontinuity at a threshold. Its properties are presented and a maximum likelihood estimation (MLE) procedure for the threshold location and jump size is developed. The distribution seems be appropriate in the context of financial engineering, production analysis, standard...

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-str...

Recent studies in the assessment of risk in maritime transportation systems have used simulation-based probabilistic techniques. Amongst them are the San Francisco Bay (SFB) Ferry exposure assessment in 2002, the Washington State Ferry (WFS) Risk Assessment in 1998 and the Prince William Sound (PWS) Risk Assessment in 1996. Representing uncertainty...

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 simulatio...

We present a construction and basic properties of a class of continuous distributions of an arbitrary form defined on a compact (bounded) set by concatenating in a continuous manner three probability density functions with bounded support using a modified mixture technique. These three distributions may represent growth, stability and decline stage...

Recent studies in the assessment of risk in maritime transportation systems have used simulation-based probabilistic techniques. Amongst them are the San Francisco Bay (SFB) Ferry exposure assessment in 2002, the Washington State Ferry (WFS) Risk Assessment in 1998 and the Prince William Sound (PWS) Risk Assessment in 1996. Representing uncertainty...

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 effecti...

The Farlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGMs with continuous marginals on a bounded support discussed in th...

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 f...

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 distrib...

An extension of the three-parameter triangular distribution utilized in risk analysis is discussed. Special cases of the resulting four-parameter family include the triangular distribution, the power function distribution and the uniform distribution. Expert judgment elicitation of its parameters is discussed as well as moment estimation and maximu...

When challenged with understanding complex, technological systems, managers often use analysis to characterize risk. Managers use this information to design projects, develop policy, and allocate resources in order to mitigate system risk. This paper presents a Bayesian risk analysis methodology for combining expert judgment with the manager's prio...

In this paper, we analyze the different weighting techniques used in the valuation theory to correct and fi t the market value of an asset with respect to the appraisals from each quality index; particularly in the valuation method of the two functions, under both independence and dependence of two quality indexes of an asset, and we expand these t...

The state of Washington operates the largest passenger vessel ferry system in the United States. In part due to the introduction of high-speed ferries, the state of Washington established an independent blue-ribbon panel to assess the adequacy of requirements for passenger and crew safety aboard the Washington state ferries. On July 9, 1998, the Bl...

The Washington State Ferries are one of the largest ferry systems in the world. Accidents involving Washington State Ferries are rare events. However, low probability, high consequence events lead to difficulties in the risk assessment process. Due to the infrequent occurrence of such accidents, large accident databases are not available for a stan...

The grounding of the Exxon Valdez caused public and government concern about the safety of oil transportation in the Prince William Sound, Alaska. As a result, a large number of proposals and recommendations were made to improve safety, but stakeholders could not achieve a consensus on their effectiveness at reducing risk. A steering committee repr...

Risk is inherent in distributed, large-scale systems. The paper explores the challenges of risk modeling in such systems, and suggests a risk modeling approach that is responsive to the requirements of complex, distributed, large-scale systems. An example of the use of the approach in the marine transportation system is given. The paper concludes w...

It will be shown that a solution exists for the parameters of a beta distribution given any combination of a lower quantile and upper quantile constraint. A numerical procedure is developed to solve for the parameters of the beta distribution given these quantile constraints. Example solutions are provided.

Risk is inherent in distributed, large-scale systems. This paper explores the challenges of risk modeling in such sys- tems, and suggests a risk modeling approach that is responsive to the requirements of complex, distributed, large-scale systems. An example of the use of the approach in the marine transportation system is given. The paper conclude...

This paper presents a new approach or methodology that effectively augments the existing nuclear criticality safety analysis techniques. It is an oblique and cost effective, yet systematic, approach which can be used to provide a facility operator one more positive assurance that the risk associated with an inadvertent criticality has been reduced...

The Prince William Sound Risk Assessment was a joint project of Det Norske Veritas (DNV), Rensselaer Polytechnic Institute (RPI), and The George Washington University (GWU). The aim of the project was to assess the baseline risk of the system and then to test the effect of proposed risk interventions on the system risk. DNV used a fault tree approa...

Monte Carlo simulation of project networks is increasingly used by engineering firms to analyze schedule/cost risk for bidding purposes. However, one serious methodological flaw of most Monte Carlo simulations is the assumption of statistical independence of activity durations in the network. In this paper, a method is proposed to model and quantif...

Monte Carlo simulation of activity networks has generated interest as a method for cost/schedule risk analysis during the design and contracting stages of large engineering projects. Commercial software for project risk analysis is now widely available as extensions to many popular project management/scheduling software packages. However, many cost...

Human error is cited as the predominant cause of transportation accidents. This paper describes the modeling of human error related accident event sequences in a risk assessment of maritime oil transportation in Prince William Sound, Alaska. The risk analysts were confronted with incomplete and misleading data that made it difficult to use theoreti...

Recently, simulation-based methods for cost/schedule risk analysis using activity networks have begun to be used by some front-running companies in manufacturing, construction, power and other industries which require internal approval and/or external bidding for multi-million dollar projects. Interest in these methods is largely due to their avail...

There is a host of literature focusing on modeling product reliability during the development phase under the title reliability growth modeling. However, these models are seldom used to address the issue of when to terminate the development process. This is important to decision makers as it is directly related to budgeting for the development proc...

The Prince William Sound (PWS) risk assessment was a joint project of Det Norske Veritas (DNV), Rensselaer Polytechnic Institute (RPI), and the George Washington University (GWU). The technique of system simulation developed by GWU was one of three risk analysis methodologies used in the PWS risk assessment. The system simulation methodology is bas...

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...

Herein, we present an overviw of the elicitation and use of expert opinion in developing optimal maintenance policies. The procedure developed is based on restrictions found in practice. That is, where the "expert" has little statistical training and the elicitation process must be performed in a clear and quick manner. Due to these restrictions, a...

T he cumulative distribution function (cdf) of a finite mixture of independent uniform random variables will be derived. The distribution is useful for uncertainty analyses in application domains such as, e.g., project risk analysis, decision analysis, finance, accident probability analysis and actuarial analysis, particularly when dependence betwe...

Copula dependence functions have shown their usefulness to environmental hydrological applications such as rainfall frequency analysis. In this paper we illustrate the utility of the Generalized Diagonal Band copula with two-sided power generating densities (GDB-TSP) in modeling rainfall return periods. Using QQ plots, in addition to, the Cramer-vo...