Knowledge database

Most risk analysis simulation software products offer Latin Hypercube Sampling (LHS). It is a method for ensuring that each probability distribution in your model is evenly sampled. The technique dates back to 1980. It was, at the time, an appealing technique because it allowed one to obtain a stable output with a much smaller number of samples than simple Monte Carlo simulation, making simulation more practical with the computing tools available at the time. However, LHS does not deserve a place in modern simulation software. In this paper we explain why.

Luminant is a Texas-based electric utility. Luminant's operations include electricity generation and wholesaling, mining, construction, and development.

Luminant wished to find a method that would optimize the maintenance and upgrade schedule for its fleet of coal-fired power units to maximize its ability to meet its delivery obligations and its ability to benefit from high seasonal spot prices whilst meeting its capital expenditure budgets.

Vose was commissioned to develop a simulation model that is continuously updated with the latest planned outage data and used reliability mathematics, coupled with historic failure rates and electricity price forecasts, to find the optimal maintenance schedule that would reduce the risk of unplanned outages in a manner that maximized revenue within the constraints of their capital expenditure budget.

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ArcelorMittal is the world’s largest steel producer, employing over 260,000 people worldwide. They face tremendous uncertainty in their business in terms of raw material, steel price and demand.

Vose has provided several services to ArcelorMittal

• Face-to-face training to employees from around the world in the techniques of quantitative risk analysis;
• Development of eLearning courses on various aspects of risk analysis that are hosted on their internal computer network. These can be viewed on PCs, Macs, and tablets;
• Assisting in the development of several risk-based evaluations.

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There arose a need for the determination of the value of an inventory of scrap metal containing precious metals. The inventory was extremely diverse, dispersed, inaccessible and largely documented, stored in a warehouse the size of several football pitches.

Vose Software was commissioned to come up with a method to estimate the inventory value and the uncertainty around that estimate. This was achieved by mapping out the site, developing a sampling plan with several stages, and building a valuation model in ModelRisk, together with a report on the methodology used.

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The Ronald Reagan Washington National Airport is a public airport 5 km south of downtown Washington, D.C. It has a series of carparks at different distances from the airport terminal.

Management had commissioned an airport consultancy firm to investigate the mix of carpark fees that would maximise revenue for the airport, accounting for the range of alternatives that the commuter has (metro, taxi, shuttle) and the mix of commuter (government, business, private).

Vose was engaged to write a risk-based model under the consultancy firm’s guidance that determined the statistically optimum pricing levels to apply across the various car parks.

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Palamon Capital Partners is a highly successful London-based private equity partnership that manages funds with €1.3 billion of equity capital for investment and is backed by some of the biggest investment institutions in the world.

Palamon typically use quantitative risk analysis models to assess prospective investments and present the risks to their funders.

Vose has supported Palamon for many years, providing training to its analysts and assisting in model building when required.

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One of the world’s largest dairy product manufacturers realised that there was potentially a risk issue with one of the ingredients it used. The risk was purely hypothetical, there was no evidence of it ever having caused harm, but they knew that if the issue was raised by the regulator, they may have to cease production while a risk assessment was prepared.

They therefore decided that they should have a professional quality risk assessment prepared in advance.

Vose was selected to perform the risk assessment because we have a long history of providing training and consulting work to most of the food regulatory agencies of the developed world. The risk analysis was a mix of highly technical biological arguments, some mathematics and statistics and some comparative reasoning.

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The US Food and Drug Administration (FDA) has the responsibility for approving new tobacco and tobacco-replacement products before they are available for commercial sale.

The guiding principle the FDA uses is that any new product should not be more harmful to human health than other similar products in the market, nor should they encourage a greater consumption than products already available. The FDA does not set out a prescriptive method for the tobacco company to demonstrate that their product meets these requirements.

RJ Reynolds, a tobacco company based in Winston-Salem, NC, had a new electronic cigarette product that it wished to present for FDA approval. They had a lot of data on the chemical yield from their own cigarettes and the new product, and access to a national database on the characteristics of US smokers.

Vose was commissioned to produce a model that FDA would find acceptable. Vose was selected because we have worked several times for the FDA and understand the methods they use for evaluating such risk assessments.

The final model provided very clear results and was mathematically extremely simple, which surprised the client, who was expecting a far more complex model. However, the comparative nature of the argument made it possible to remove a number of factors. In addition, some special simulation techniques were applied to ensure an ‘apples with apples’ comparison that then gave a very clear comparison of the two products.

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Dr. Reddy's Laboratories Ltd, is a pharmaceutical company based in Hyderabad, India. Dr. Reddy's manufactures and markets a wide range of pharmaceuticals in India and overseas. The company has over 190 medications, 60 active pharmaceutical ingredients for drug manufacture, diagnostic kits, critical care, and biotechnology products.

The head of enterprise risk management – finance wished to bring more quantitative risk analysis methods into their processes. He approached Vose to provide the appropriate risk modeling training and software.

Logistics meant that the training course needed to be delivered online. After discussing the work that they undertake and the risk issues they wanted to focus on, Vose provided a draft overview of the training topics that could be given: topics like expert elicitation of uncertainty, time series forecasting, fitting distributions to data, options evaluation, etc. The draft was discussed and mapped to their specific needs. Once agreed upon, we were able to edit our standard training material to use examples and problems that would resonate with Dr Reddy’s, and incorporate some data they shared.

The course was delivered over four half-days using GoToWebinar. A recording of each session was made and provided to the client, together with the example models. The course was very cost-efficient, requiring a total of just five days billed time and no travelling or accommodation expenses.

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Campylobacter is a bacterium that is the most frequent cause of foodborne illness in Europe - an estimated 190,000 cases a year (and 1.3 million cases a year in the US). The greatest exposure consumers have to Campylobacter is via poultry meat contaminated with (tiny amounts of) the bird’s feces.

The European Food Safety Authority (EFSA) is an agency of the European Union, based in Parma, Italy, that provides independent scientific advice and communication on existing and emerging risks associated with the food chain.

Vose won a competitive tender to produce a European-wide risk assessment model that would allow EFSA’s Campylobacter panel to evaluate various potential interventions to reduce the level of illness.

The task was particularly challenging because the model needed to normalize to data on prevalence of contamination and bacterial concentrations at two points along the farm-to-consumer continuum: the poultry sheds, and the slaughter plants; as well as the estimated number of attributable illnesses. This meant that the usual Monte Carlo simulation approach was not possible. It also needed to produce informative results in the face of a highly uncertain dose-response relationship.

Vose’s solution was to create a model that used probability identities derived from statistics called raw moments, coupled with numerical integration techniques. The resultant model, built in ModelRisk, mathematically calculated the fractional change in human illness due to different interventions, and simulation was then applied to this deterministic model to describe uncertainties for the various model parameters.

The model was contentious, because it did not comply with the usual methods employed by food safety risk analysts. However, unlike most food safety risk assessments, it was able to provide high quality responses to all the questions posed by the EFSA panel.

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Salmonella is a bacterium that is the second most frequent cause of foodborne illness in Europe - estimated to be over 100,000 cases a year (and 1.2 million cases a year in the US). Salmonellosis can result in hospitalization and, in about 0.04% of cases – death.

Humans are exposed to Salmonella from several sources – fecally-contaminated meat from chickens, turkeys, ducks, pigs, and cows being the most important, as well as eggs.

Salmonella is a very hardy bacterium, so it can contaminate vegetables fertilized with manure, and can be present in rivers and lakes in which people swim from runoff from fields. It can also grow in normal environmental conditions.

This makes it extremely difficult to pinpoint the original source of the bacteria. However, Salmonella can be identified as belonging to a specific sero- or phage-type, of which there are many. Moreover, the proportions of these sero-and phage-types are very different among the various animal species.

As a result, it is possible to match the typing patterns of these bacteria in human cases of illness with the typing patterns in animals. This was first demonstrated in an academic paper we co-authored.

The European Food Safety Authority (EFSA) commissioned us, after a tendering process, to produce an attribution assessment that would identify the main sources of Salmonella by food type and country. The problem was made more complex by the widespread and unregulated movement of animal products between Member States.

Vose produced a Markov Chain Monte Carlo model using the OpenBugs software. The model was able to normalize to the data set for one year and accurately predict the illness patterns for the following year, giving us a good level of confidence in its robustness. The model provided EFSA’s expert panel with all the answers they required.

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Century Aluminum, based in Kentucky, is one of the largest aluminum smelters in the US. Aluminum manufacture begins with bauxite ore, which is melted down in ‘pots’ together with a variety of other material to help conductivity and electrolysis.

When the ‘pots’ have been cooked sufficiently, the content is poured into larger vessels called ‘cruces’. The material from the cruces is poured into ingot and pig moulds and sold to manufacturers.

The price of an ingot depends on the level of purity, mostly silicon and iron. Century Aluminum wanted a model that it could run before each filling of a cruce that would determine the mixing of pots into cruces that would maximize the value of the end product.

A complication was that measures of purity levels in each pot are inexact. The model therefore needed to account for uncertainty and optimize to achieve the highest value at a particular level of confidence. The model also needed to incorporate other production constraints. Vose built the required model using the stochastic optimizer from ModelRisk, constructed the logic to allow it to optimize extremely quickly, and built an interface so the end-user could enter the pots’ purity characteristics, hit ‘run’ and be told the fraction of each pot to be placed in the cruces.

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21st Century Insurance is an auto insurance company headquartered in Wilmington, Delaware, and provide private passenger auto insurance in 48 states and the District of Columbia.

21st Century Insurance wished to improve its staffing levels at its call Spanish and English language centers. It observed patterns in traffic that followed a daily pattern but that exhibited significantly differences between languages and around vacation periods.

Vose was commissioned to develop an analysis. The project consists of two parts: the first was to review, enhance and further develop an existing model to forecast total call volume for the coming year. The results from this model were used to support their management of staffing levels and training.

The second part was to develop a model that forecast call volumes over the following month in ½ hour increments, broken down into a number of territories, as well as language, to help plan short-term staffing levels.

The project involved a considerable amount of statistical analysis of historic call rates, and revealed interesting and perhaps unexpected patterns. For example, it showed that there were peaks both just before and just after a national holiday, but the average traffic was the same as other periods in the year, and the proportion who called before or after was markedly different according to language. It also showed the effect of daylight saving (Arizona and Hawaii do not apply daylight saving so their call profile shifts by an hour relative to the other states) which also change on different dates each year.

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Grindrod Bank is a commercial bank in the Republic of South Africa with a total asset base in excess of US$550 million.

Grindrod commissioned Vose to develop a simulation model using ModelRisk to estimate the distribution of the amount of time that a nominal portfolio of assets would support the constant cash drawdown of a pension. The model was based on a mix of assets defined by the client, with a formula specified by the client for defining the growth in asset value and generation of revenue. The model included a pre- and post-retirement phase reflecting growth and depletion of the portfolio respectively.

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A solar flare is a sudden, rapid, and intense variation in brightness of the sun. It occurs when magnetic energy that has built up in the solar atmosphere is suddenly released. Radiation is emitted across virtually the entire electromagnetic spectrum. The amount of energy released is the equivalent of millions of 100-megaton hydrogen bombs exploding at the same time.

NASA investigates the characteristics of these flares as they can, for example, cause damage and disruption to satellites. There are strong, idiosyncratic patterns in the frequencies of different particles emitted in the flare that NASA wished to model.

Vose helped NASA apply the special Data Copula feature in its ModelRisk software to solve this problem. The Data Copula has the ability to statistically assess and model correlation patterns of any form across any number of random variables. By using our Data Copula capability, NASA is able to provide a far more precise prediction of solar flare activity than would have been possible using the correlation tools of competing products to ModelRisk.

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Bruce Power, based in Ontario, Canada operates the world’s largest nuclear power facility. They required a model that they could use on an ongoing basis to forecast the amount of power they could generate that would incorporate planned and unplanned outages.

Vose performed a statistical analysis of their historic outages, assessing the types of random processes involved and any correlation. The fitted statistical models included parameter uncertainty – a vital component to fully assess the uncertainty of the forecasts.

Vose then created a spreadsheet risk model that could be updated with new outage data, automatically evaluate any new trends, and that would produce up-to-date forecasts of their power generation.

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Spectra Energy, an S&P 500 company, transmits and stores natural gas, operating one of the largest pipeline systems in the United States. They commissioned Vose to assist them in assessing the project schedule and cost risks for a new $500M+ liquid natural gas pipeline.

Vose provided training for their risk analysis team in quantitative risk analysis techniques, harmonizing their various risk reporting processes, and applying these to the new project.

We then led them through the project risk analysis and developed sub-models that they could reproduce in similar circumstances that evaluated such issues as change in planned routes due to geological conditions or lack of planning approval.

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