The Case for Truly Integrated Cost and Schedule Risk Analysis

Schedule risk and cost risk analyses use statistical techniques to predict a level of confidence in meeting a program’s completion date and cost. This paper describes how to interpret key Schedule Risk Analysis (SRA) and Cost Risk Analysis (CRA) results to determine the likelihood that the program completion dates are met, how much management reserve (MR) is needed to provide the acceptable certainty of completion by a specific date, and the risks and activities that are most likely to delay or add cost to a project. The combined process is often called a Schedule/Cost Uncertainty and Risk Analysis or “SCURA.”

As part of Weapon Design Cost Report (WDCR), LLNL will be performing site Schedule Risk and Cost Risk Analysis. This analysis uses statistical techniques to predict a level of confidence in meeting the program’s completion date. This document includes the process and steps to conduct the Schedule Risk and Cost Risk Analysis to determine the likelihood that the program completion date are met, how much management reserve is needed to provide the acceptable certainty of completion by a specific date, risks most likely to delay the project, and the paths or activities that are most likely to delay the program. The analysis focuses on uncertainty and key risks and how they affect the schedule’s activity durations and established a management reserve.

Preface. 1 Introduction. 1.1 The Importance of Risk and Uncertainty Assessments. 1.2 The Need to Develop a Proper Risk Analysis Framework. Bibliographic Notes. 2 Common Thinking about Risk and Risk Analysis. 2.1 Accident Risk. 2.1.1 Accident Statistics. 2.1.2 Risk Analysis. 2.1.3 Reliability Analysis. 2.2 Economic Risk. 2.2.1 General Definitions of Economic Risk in Business and Project Management. 2.2.2 A Cost Risk Analysis. 2.2.3 Finance and Portfolio Theory. 2.2.4 Treatment of Risk in Project Discounted Cash Flow Analysis. 2.3 Discussion and Conclusions. 2.3.1 The Classical Approach. 2.3.2 The Bayesian Paradigm. 2.3.3 Economic Risk and Rational Decision-Making. 2.3.4 Other Perspectives and Applications. 2.3.5 Conclusions. Bibliographic Notes. 3 How to Think about Risk and Risk Analysis. 3.1 Basic Ideas and Principles. 3.1.1 Background Information. 3.1.2 Models and Simplifications in Probability Considerations. 3.1.3 Observable Quantities. 3.2 Economic Risk. 3.2.1 A Simple Cost Risk Example. 3.2.2 Production Risk. 3.2.3 Business and Project Management. 3.2.4 Investing Money in a Stock Market. 3.2.5 Discounted Cash Flow Analysis. 3.3 Accident Risk. Bibliographic Notes. 4 How to Assess Uncertainties and Specify Probabilities. 4.1 What Is a Good Probability Assignment? 4.1.1 Criteria for Evaluating Probabilities. 4.1.2 Heuristics and Biases. 4.1.3 Evaluation of the Assessors. 4.1.4 Standardization and Consensus. 4.2 Modelling. 4.2.1 Examples of Models. 4.2.2 Discussion. 4.3 Assessing Uncertainty of Y. 4.3.1 Assignments Based on Classical Statistical Methods. 4.3.2 Analyst Judgements Using All Sources of Information. 4.3.3 Formal Expert Elicitation. 4.3.4 Bayesian Analysis. 4.4 Uncertainty Assessments of a Vector X. 4.4.1 Cost Risk. 4.4.2 Production Risk. 4.4.3 Reliability Analysis. 4.5 Discussion and Conclusions. Bibliographic Notes. 5 How to Use Risk Analysis to Support Decision-Making. 5.1 What Is a Good Decision? 5.1.1 Features of a Decision-Making Model. 5.1.2 Decision-Support Tools. 5.1.3 Discussion. 5.2 Some Examples. 5.2.1 Accident Risk. 5.2.2 Scrap in Place or Complete Removal of Plant. 5.2.3 Production System. 5.2.4 Reliability Target. 5.2.5 Health Risk. 5.2.6 Warranties. 5.2.7 Offshore Development Project. 5.2.8 Risk Assessment: National Sector. 5.2.9 Multi-Attribute Utility Example. 5.3 Risk Problem Classification Schemes. 5.3.1 A Scheme Based on Potential Consequences and Uncertainties. 5.3.2 A Scheme Based on Closeness to Hazard and Level of Authority. Bibliographic Notes. 6 Summary and Conclusions. Appendix A: Basic Theory of Probability and Statistics. A.1 Probability Theory. A.1.1 Types of Probabilities. A.1.2 Probability Rules. A.1.3 Random Quantities (Random Variables). A.1.4 Some Common Discrete Probability Distributions (Models). A.1.5 Some Common Continuous Distributions (Models). A.1.6 Some Remarks on Probability Models and Their Parameters. A.1.7 Random Processes. A.2 Classical Statistical Inference. A.2.1 Non-Parametric Estimation. A.2.2 Estimation of Distribution Parameters. A.2.3 Testing Hypotheses. A.2.4 Regression. A.3 Bayesian Inference. A.3.1 Statistical (Bayesian) Decision Analysis. Bibliographic Notes. Appendix B: Terminology. Bibliography. Index.

Thermal-pulse method is a powerful tool for measuring space charge distributions in polymer films. The data analysis for thermal-pulse method involves the Fredholm integral equation of the first kind, which requires an appropriate numerical procedure to obtain a solution. Various numerical techniques, including scale transformation and regulation method, are proposed. Of those numerical methods, the scale transformation (ST) is the simplest and the most widely used method. However, it presents a high spatial resolution only near the sample surface. Monte Carlo (MC) method is one of the recently proposed ways to solve the equation numerically and has been successfully applied to the analysis of laser intensity modulation method data, which also involves the Fredholm integral equation of the first kind. In this paper we attempt to analyze thermal-pulse data in frequency domain with the MC method and discuss its effectiveness based on some numerical simulations. The simulation results indicate that the electric field profiles can be effectively extracted by the MC method. The computed profiles by the MC method consist well with the supposed distributions in the entire thickness of the sample, while the profiles reconstructed by the ST method fit very well to the supposed one at the vicinity of the target surface and distort sharply along the direction of the thermal pulse propagation in the sample bulk. On the other hand, the oscillations in the computed results by the MC method could deteriorate its accuracy in this study. The influence of noise level on the analysis based on the MC method is also tested by the use of the simulated data. The results show that the computed profiles would become more fluctuant as the noise level increases. This problem can be solved by selecting a larger value of tolerance during the singular value decomposition procedure. Thus, the value of tolerance is considered to be one of the key parameters in this algorithm, which is actually hard to determine. Additionally, the experimental data obtained from a polypropylene film under applied electric field are analyzed to illustrate the feasibility of MC method to be applied to the thermal-pulse experimental data. The results also show that the spatial accuracy by the MC method in the entire sample thickness is higher than by the ST method, which verifies that the MC method is more suitable for detecting the electric field distribution in the deep bulk of the sample. Owing to noise and error, the accuracy of MC calculation depends on the chosen tolerance value, which is now considered to be an obstacle in applying this method to the practical thermal-pulse measurement.

Part 1 Concepts and Inputs: Projectability Concepts Evaluation Types and Data Needs Depreciation and Income Taxes Comparing Individual Project and Corporate Returns. Part 2 Discounted Cash Flow Calculations: Discounted Cash Flow Techniques Comparing Alternatives Handling Inflation Replacement Cost and Lease Analysis Risk Analysis by Project Sensitivities Other Risk Analysis Techniques Shortcut Techniques for Economic Evaluations. Part 3 Reporting Results: Types of Economic Reports Postinstallation Appraisals Case Problem. Appendices: Glossary of Selected Financial Terms Accounting Financial Statements Cost of Capital AACE Classification System for Economic Appraisals Nondiscounted Techniques Inflation Theory Deviation of Shortcut Correlation Equations Instructions for Preparing an Appraisal Report Solution to the Case Problem. Discount Factor Tables.

The recent rise of integrated risk analyses methods has created a new opportunity for complex projects to understand the dynamic inter-relationship of cost, schedule, and risk. NASA has been implementing Joint Confidence Level (JCL) analysis of cost, schedule, and risk for all major projects since 2009 in an attempt to proceduralize and codify the requirements for an integrated risk analysis product. Since the method of integrated risk analysis is itself new, the visualization of analysis results has been challenging. Starting with the simple X-Y scatter plot, this paper will explain how to understand the results of an integrated cost/schedule risk analysis using illustrative examples. The authors will also propose new advanced methods for visualizing results, and provide evidence of the valuable insight that can be gained from conducting an integrated cost/schedule risk analysis.

The success of major capital projects hinges on the balance between revenue and expenditure. Integrated Cost & Schedule Risk Analysis (iCSRA) emerges as a critical tool for enhancing predictability and mitigating risks associated with project delays and cost overruns. This paper explores the impact of iCSRA on project outcomes, drawing on actual performance data openly published by the Norwegian Offshore Directorate and other industry benchmarks. Key findings reveal that a significant proportion of projects exceed budget and schedule estimates at Final Investment Decision (FID), with only one in seven (14%) experiencing cost and schedule underruns. iCSRA helps address these challenges by providing a probabilistic approach to risk management, enabling better alignment of project teams and more informed decision-making. The methodology involves detailed risk identification, probabilistic modelling, and collaborative workshops to refine project schedules and cost estimates. The paper underscores the importance of robust data inputs and the need to account for biases and uncertainties in risk assessments. By integrating cost and schedule risks, iCSRA offers a comprehensive view of project uncertainties, facilitating more accurate predictions and effective risk mitigation strategies. The ultimate goal is to maximize project success by improving the confidence level in achieving both cost and schedule targets, thereby enhancing the overall value and credibility of projects.

Schedule risk analysis for new-product development: The GERT method extended by a characteristic function

A tool to test and validate algorithms for the resource-constrained project scheduling problem

Construction projects are inherently associated with various risks that can increase the project costs. Identifying and analyzing such risks are essential to successfully managing construction budgets at state Departments of Transportation (DOTs). While many state DOTs have developed and/or adopted risk assessments methodologies and tools, Tennessee DOT (TDOT) lacks a comprehensive methodology and tool to analyze construction project risks. This study reviewed state DOT practices of analyzing various risks associated with large infrastructure construction projects. The comparison of risk assessment practices among state DOTs are summarized in three sections: a) risk management, b) major categories affecting project costs, and c) risk estimating tools and practices. The review finds that many state DOTs have similar practices of analyzing project risks and have developed spreadsheet-based tools to automate such analysis. While some risk analysis tools are used primarily for qualitative risk analysis, other tools are developed for qualitative and quantitative risk analysis. Such tools with qualitative and quantitative risk analysis can be used to quantify contingencies for various projects for budgeting purposes.

Background Small megavoltage photon fields are increasingly used in modern radiotherapy techniques such as stereotactic radiotherapy. Therefore, it is important to study the reliability of dosimetry in the small-field conditions. The IBA Razor Nano Chamber (Nano chamber) ionization chamber is particularly intended for small-field measurements. In this work, properties of the Nano chamber were studied with both measurements and Monte Carlo (MC) simulations. Material and methods The measurements and MC simulations were performed with 6 MV, 6 MV FFF and 10 MV FFF photon beams from the Varian TrueBeam linear accelerator. The source-to-surface distance was fixed at 100 cm. The measurements and MC simulations included profiles, percentage depth doses (PDD), and output factors (OF) in square jaw-collimated fields. The MC simulations were performed with the EGSnrc software system in a large water phantom. Results The measured profiles and PDDs obtained with the Nano chamber were compared against IBA Razor Diode, PTW microDiamond and the PTW Semiflex ionization chamber. These results indicate that the Nano chamber is a high-resolution detector and thus suitable for small field profile measurements down to field sizes 2 × 2 cm2 and appropriate for the PDD measurements. The field output correction factors and field OFs were determined according to TRS-483 protocol In the 6 MV FF and FFF beams, the determined correction factors were within 1.2% for the field sizes of 1 × 1 cm2–3 × 3 cm2 and the experimental and MC defined field output factors showed good agreement. Conclusion The Nano chamber with its small cavity volume is a potential detector for the small-field dosimetry. In this study, the properties of this detector were characterized with measurements and MC simulations. The determined correction factors are novel results for the NC in the TrueBeam fields.

In these days, Monte Carlo (MC) simulation is a method that can calculate the radiation dose that occurs in an environment in the most accurate way. The correct measurement of the dose occurring on the patient’s surface is of great importance to estimate the reactions that may occur on the patient’s skin. This importance encouraged us to do this study. The aim of this study is to determine buildup region and surface doses using MC simulation and to compare them with results of the parallel plane ion chamber and Treatment Planning System (TPS) measurements for 6-MV photon beams. Surface doses normalized to the maximum dose for the parallel plane ion chamber, MC simulation, fast photon (FP) algorithm, and collapsed cone convolution superposition (CC) algorithm are 13.6%, 30.28%, 0%, and 27.33%, respectively. The CC algorithm and parallel plane ion chamber measurements are compatible with MC simulation but the FP algorithm has calculated the dose less to a depth of 0.8 cm. Measuring the surface dose and the doses in the buildup region is of great importance in terms of accurately predicting the complications that may occur in the patient’s skin and taking precautions early. Using some methods and correction factors, the surface dose and the doses that may occur in the buildup region can be accurately calculated. It is recommended not to use the FP algorithm for stereotactic body radiation therapy and intensity-modulated radiation therapy treatments, as it cannot calculate doses correctly in the buildup region and surface.

On the assessment of economic risk: factorial design versus Monte Carlo methods

Purpose: To create a Monte Carlo (MC) model of an ocular proton therapy device, or ocular nozzle, that can predict relative doses to within 3% or 0.5 mm, D/MU values, and be used to develop and commission an analytical algorithm to predict doses and D/MU values to within similar criteria. Methods and Materials: Depth dose profiles and D/MU values were measured in eight ocular proton therapy fields including four unmodulated and four modulated beams using a parallel‐plane ionization chamber in water. Crossfield profiles were measured at three or more depths for each of the modulated beams using film. A MC model of the ocular nozzle was constructed using the MCNPX radiation transport code. After benchmark tests against the measurements, the MC model was used to provide dosimetric data needed to develop a broad‐beam algorithm capable of predicting relative and absolute doses and to test the algorithm's predictions more comprehensively than could be afforded with measured data. Specifically, MC and analytical predictions were calculated and compared in two‐dimensions in a water phantom and in an anthropomorphic model of the eye. Results: Relative depth dose profiles between MC and measurements agreed to within 3% or 0.5 mm. MC predicted D/MU values agreed to within 1% of the measured values. Similarly, the analytical algorithm accurately predicted dose distributions where the predictions were generally within 3% or 0.5 mm of measured and simulated values at water depth > 6 mm. At shallower depths, the analytical model underestimated the dose by approximately 3% to 6%, which MC simulations revealed was due to edge‐scattered protons from the nozzle's collimators. Conclusion: The MC model accurately predicted dose distributions and D/MU values in ocular proton therapy beams. Furthermore, the present work demonstrates the value of the MC method for developing and testing contemporary analytical dose algorithms.

As energy demand increases and global warming progresses, expectations for fuel cells, which generate electricity through chemical reactions between hydrogen and oxygen, are rising. There are various types of fuel cells, which are classified according to the electrolyte. Polymer electrolyte fuel cells (PEFCs) are expected to be used in stationary power sources for home use and fuel cell vehicles because of their low operating temperature, short start-up time, and ease of miniaturization. The cost has been an issue in the widespread use of fuel cells. The amount of platinum used in the catalyst layer (CL) must be reduced to reduce costs. However, it increases the current density per unit area of platinum. There are three factors that contribute to voltage drop: ohmic polarization, activation polarization, and diffusion polarization. At high current densities, the voltage drop due to diffusion polarization is dominant. The main cause of diffusion polarization is the transport resistance of oxygen molecules in the CL, and improving the oxygen transport properties in the CL will lead to lower cost PEFCs. In this study, we analyzed the transport properties of oxygen molecules in the CLs of PEFCs using the Monte Carlo (MC) method. The effect of oxygen scattering on the overall oxygen transport properties was investigated by considering the behavior on the surface of the ionomer film (surface diffusion) into the MC method, which simulates the overall transport in the PEFC CL. The objective of this study is to reproduce accurate oxygen transport by comparing the results of MC and molecular dynamics (MD) methods. First, we used the MC method to analyze oxygen scattering phenomena. In this study, we used the 3D structure data of CL in the MC simulations. The three-dimensional structure of the sample was reconstructed from sequential slice images. Molecules were assumed to reflect specularly on the boundaries of the simulation domain. Oxygen molecules were randomly placed in the simulation system. The time step was set at 5 ps and the simulation time was set at 4 μs. In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using various conditions of surface diffusion. We calculated the effective diffusion coefficient of oxygen in the CL as the transport property of oxygen molecules in the MC method. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the effective diffusion coefficient of oxygen increases due to a decrease in the time constant, which determines the probability distribution of the surface residence time. However, when the surface diffusion coefficient is large, a different trend emerges. As the time constant increases, the effective diffusion coefficient has a peak value and then decreases. Next, to verify the model of surface diffusion in the MC method, we analyzed the scattering phenomenon of oxygen molecules in a simulation system that simulates the pores in the CL using the MD method. We modeled the nano pores in the CL as a slit between the ionomer walls in the MD method. Nafion with the equivalent weight (EW) of 1146 was used as polymer model. The number of Nafion chains is set at 4, and the water content λ is set at 7. Three-dimensional periodic boundary conditions were applied to the simulation domain. After the system was equilibrated, 1 ns of NVT simulation was performed for production. The temperature was set at 297 K. The behavior of oxygen molecules impacting on the ionomer wall was analyzed. We analyzed the behavior of oxygen molecules colliding with the ionomer membrane using the MD method. The average residence time of surface diffusion on the ionomer thin film was of the order of 10-10s. When the calculation results were compared with the MC results, it was found that the average residence time obtained by the MD method was the value where the surface diffusion coefficient affects much on the effective diffusion coefficient. Comparing the results of the MD method with the surface diffusion model used in the MC method, there are some discrepancies between the results and the model. For example, the MC method used a model in which oxygen molecules reflect diffusively on the ionomer surface. However, in the MD method, it was found that oxygen molecules tend to reflect in the direction of travel (Fig. 1). Therefore, a more accurate model of the MC method needs to be developed in the future. Figure 1