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Evaluating warfighter lethality is a critical aspect of military performance. Raw metrics such as marksmanship speed and accuracy can provide some insight, yet interpreting subtle differences can be challenging. For example, is a speed difference of 300 milliseconds more important than a 10% accuracy difference on the same drill? Marksmanship evaluations must have objective methods to differentiate between critical factors while maintaining a holistic view of human performance.

Monte Carlo simulations are one method to circumvent speed/accuracy trade-offs within marksmanship evaluations. They can accommodate both speed and accuracy implications simultaneously without needing to hold one constant for the sake of the other. Moreover, Monte Carlo simulations can incorporate variability as a key element of performance. This approach thus allows analysts to determine consistency of performance expectations when projecting future outcomes.

The review divides outcomes into both theoretical overview and practical implication sections. Each aspect of the Monte Carlo simulation can be addressed separately, reviewed and then incorporated as a potential component of small arms combat modeling. This application allows for new human performance practitioners to more quickly adopt the method for different applications.

Performance implications are often presented as inferential statistics. By using the Monte Carlo simulations, practitioners can present outcomes in terms of lethality. This method should help convey the impact of any marksmanship evaluation to senior leadership better than current inferential statistics, such as effect size measures.

The purpose of this paper is to deal with the appropriateness of using the Monte Carlo simulation as a technique to calculate risk in real estate development.

The paper is divided into two interlinked segments. The first segment examines the general definition of risk and Monte Carlo simulation methodology as a tool to estimate risk. The second outlines the appropriateness of using Monte Carlo as a tool to model real estate development, given the lack of data quality and its inability to account for human relationships in the development process.

It is important that the Monte Carlo Simulation model is used as prescriptive model that builds on the original elicitation procedures; produces initial results; allows for detailed sensitivity analysis and then remodels as required. In short, to be fully effective, the Monte Carlo Simulation model needs to be used in a complementary fashion with an understanding of human judgement and decision making.

A fuller analysis may include an examination of the uncertainties in each of the components of the appraisal and account for the appropriate distributions of each of these variables. This is generally referred to as a Monte Carlo simulation. The argument in favour of a Monte Carlo simulation is that it helps the appraiser have a better understanding of the possible outcomes for the development and the relative impact of each input in the pricing of the project.

A lot of work has been done looking at scenario modelling with probabilities and the results that ensue. However, it is important that these quantitative results are placed in the context of the heuristic and cognitive approaches adopted by the decision maker. In other words, the behaviour of the decision maker is as influential in the interpretation of the results as the numbers themselves. This paper looks at the advantages and disadvantages of using Monte Carlo simulation in this context.

This study contributes significantly to the practical application of probability‐based models to development appraisal. The findings of the study are useful for users of feasibility studies to understand the context in which a development feasibility is carried out, and for appraisers to extend the scope of their analysis when carrying them out.

A numerical integration scheme using the Monte Carlo method is discussed to evaluate the singular integral in boundary elements. A numerical demonstration is given for some potential problems. Results evaluated by the Monte Carlo method are compared with the analytical ones for accuracy and computation time. Examination shows the validity and capability of the approach.

In smaller projects with limited resources, schedule updates are often not performed. In these situations, traditional delay analysis methods cannot be used as they all require updated schedules. The objective of this study is to develop a model that performs delay analysis by using only an as-planned schedule and the expense records kept on site.

This study starts out by developing an approach that estimates activity duration ranges in a network schedule by using as-planned and as-built s-curves. Monte Carlo simulation is performed to generate candidate as-built schedules using these activity duration ranges. If necessary, the duration ranges are refined by a follow-up procedure that systematically relaxes the ranges and develops new as-built schedules. The candidate schedule that has the closest s-curve to the actual s-curve is considered to be the most realistic as-built schedule. Finally, the as-planned vs. as-built delay analysis method is performed to determine which activity(ies) caused project delay. This process is automated using Matlab. A test case is used to demonstrate that the proposed automated method can work well.

The automated process developed in this study has the capability to develop activity duration ranges, perform Monte Carlo simulation, generate a large number of candidate as-built schedules, build s-curves for each of the candidate schedules and identify the most realistic one that has an s-curve that is closest to the actual as-built s-curve. The test case confirmed that the proposed automated system works well as it resulted in an as-built schedule that has an s-curve that is identical to the actual as-built s-curve. To develop an as-built schedule using this method is a reasonable way to make a case in or out of a court of law.

Practitioners specifying activity ranges to perform Monte Carlo simulation can be characterized as subjective and perhaps arbitrary. To minimize the effects of this limitation, this study proposes a method that determines duration ranges by comparing as-built and as-planned cash-flows, and then by systematically modifying the search space. Another limitation is the assumption that the precedence logic in the as-planned network remains the same throughout construction. Since updated schedules are not available in the scenario considered in this study, and since in small projects the logic relationships are fairly stable over the short project duration, the assumption of a stable logic throughout construction may be reasonable, but this issue needs to be explored further in future research.

Delays are common in construction projects regardless of the size of the project. The critical path method (CPM) schedules of many smaller projects, especially in developing countries, are not updated during construction. In case updated schedules are not available, the method presented in this paper represents an automated, practical and easy-to-use tool that allows parties to a contract to perform delay analysis with only an as-planned schedule and the expense logs kept on site.

Since an as-built schedule cannot be built without updated schedules, and since the absence of an as-built schedule precludes the use of any delay analysis method that is acceptable in courts of law, using the method presented in this paper may very well be the only solution to the problem.

We present a generalized self‐scattering method for generating carrier free flight times in Monte Carlo simulation. Compared to traditional approaches, the added flexibility of this approach results in fewer fictitious scatterings, which is especially appealing for load balance and efficiency when a SIMD parallel computer is used. Speedups from 19% to 69% over an optimized variable‐Γ approach are shown for an implementation on the Connection Machine CM‐2. The performance sensitivities to applied fields and grid spacings are also presented. The conversion of existing variable‐Γ software to this new approach requires only a few changes.

The robust appraisal of exploration drilling concepts is essential for establishing the economic viability of a prospective recovery field. This study evaluates the different concept selection methods that were considered for drilling operations at the Trym field in Norway. The construction of drilling rigs is a capital-intensive process, and it involves high levels of economic risk. These risks can be broadly categorised as aleatoric (i.e. those related to chance) and epistemic (i.e. those related to knowledge). Evaluating risks in the investment appraisal process tends to be a complicated process. Project risks are evaluated using Monte Carlo simulation (MCS) and are based on the fuzzy analytic hierarchy process (AHP). MCS provides a useful means of evaluating variabilities (i.e. aleatoric risks) in oil drilling operations. However, many of the economic risks in oil drilling processes are unanticipated, and, in some cases, are not readily expressible in quantitative values. The fuzzy AHP is therefore used to appraise the qualitatively defined indirect revenues comprising risks that affect future flexibilities, schedule certainty and health and safety performance. Both the Monte Carlo technique and the fuzzy AHP technique found that a cumulative revenue variation of up to 30% is possible in any of the considered drilling options. The fuzzy AHP technique estimates that the chances of profitability being less than NOK 1 billion over a five-year period is 0.5%, while the Monte Carlo technique estimates suggest a more conservative proportion of 10%. Overall, the fuzzy AHP technique is easy to use and flexible, and it demonstrates increased robustness and improved predictability.

The purpose of this paper is to propose a bearing replacement strategy which employs the Monte Carlo simulation method. In this contribution the method is used to estimate the economic impact on the selection of a particular bearing change strategy. The simulation demonstrates that it is possible to identify the most cost‐effective approach and thus suggests a suitable bearing replacement policy, which in turn allows engineers to develop the appropriate maintenance schedules for their company.

The paper develops the Monte Carlo method through a case study approach. Three case studies are presented. The first study is detailed and chronicles the design, development and implementation of the Monte Carlo method as a means of defining a bearing replacement strategy within a subject company. The second and third cases outline the application of the Monte Carlo method in two different environments. These applications made it possible to obtain proof of concept and also to further prove the effectiveness of the Monte Carlo simulation approach.

An effective development of the Monte Carlo approach is proposed and the effectiveness of the method is subsequently evaluated, highlighting the benefits to the host organization and how the approach led to significant improvement in machinery reliability through a bearing replacement strategy.

The design, development and implementation of a bearing replacement strategy provide a simple yet effective approach to achieving significant improvements in system reliability and performance through less downtime and greater cost savings. The paper offers practising maintenance managers and engineers a strategic framework for increasing productive efficiency and output.

The proposed bearing replacement strategy contributes to the existing knowledge base on maintenance systems and subsequently disseminates this information in order to provide impetus, guidance and support towards increasing the development companies in an attempt to move the UK manufacturing sector towards world‐class manufacturing performance.

Marksmanship data is a staple of military and law enforcement evaluations. This ubiquitous nature creates a critical need to use all relevant information and to convey outcomes in a meaningful way for the end users. The purpose of this study is to demonstrate how simple simulation techniques can improve interpretations of marksmanship data.

This study uses three simulations to demonstrate the advantages of small arms combat modeling, including (1) the benefits of incorporating a Markov Chain into Monte Carlo shooting simulations; (2) how small arms combat modeling is superior to point-based evaluations; and (3) why continuous-time chains better capture performance than discrete-time chains.

The proposed method reduces ambiguity in low-accuracy scenarios while also incorporating a more holistic view of performance as outcomes simultaneously incorporate speed and accuracy rather than holding one constant.

This process determines the probability of winning an engagement against a given opponent while circumventing arbitrary discussions of speed and accuracy trade-offs. Someone wins 70% of combat engagements against a given opponent rather than scoring 15 more points. Moreover, risk exposure is quantified by determining the likely casualties suffered to achieve victory. This combination makes the practical consequences of human performance differences tangible to the end users. Taken together, this approach advances the operations research analyses of squad-level combat engagements.

For more than a century, marksmanship evaluations have used point-based systems to classify shooters. However, these scoring methods were developed for competitive integrity rather than lethality as points do not adequately capture combat capabilities. The proposed method thus represents a major shift in the marksmanship scoring paradigm.

The purpose of this paper is to expose computational methods as applied to engineering systems and evolutionary processes with randomness in external actions and inherent parameters.

In total, two approaches are distinguished that rely on solvers from deterministic algorithms. Probabilistic analysis is referred to as the approximation of the response by a Taylor series expansion about the mean input. Alternatively, stochastic simulation implies random sampling of the input and statistical evaluation of the output.

Beyond the characterization of random response, methods of reliability assessment are discussed. Concepts of design improvement are presented. Optimization for robustness diminishes the sensitivity of the system to fluctuating parameters.

Deterministic algorithms available for the primary problem are utilized for stochastic analysis by statistical Monte Carlo sampling. The computational effort for the repeated solution of the primary problem depends on the variability of the system and is usually high. Alternatively, the analytic Taylor series expansion requires extension of the primary solver to the computation of derivatives of the response with respect to the random input. The method is restricted to the computation of output mean values and variances/covariances, with the effort determined by the amount of the random input. The results of the two methods are comparable within the domain of applicability.

The present account addresses the main issues related to the presence of randomness in engineering systems and processes. They comprise the analysis of stochastic systems, reliability, design improvement, optimization and robustness against randomness of the data. The analytical Taylor approach is contrasted to the statistical Monte Carlo sampling throughout. In both cases, algorithms known from the primary, deterministic problem are the starting point of stochastic treatment. The reader benefits from the comprehensive presentation of the matter in a concise manner.

The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind.

A numerical algorithm consisted of the combined use of the successive substitution method and Monte Carlo simulation is established for the solution of Fredholm integral equations of the second kind.

Owing to the application of the present method, the variance of the solution is reduced. Therefore, this method achieves several orders of magnitude improvement in accuracy over the conventional Monte Carlo method.

Numerical tests are performed in order to show the efficiency and accuracy of the present paper. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes CPU time at Pentium IV‐2.4 GHz PC.

This paper provides a new efficient method to solve Fredholm integral equations of the second kind and discusses basic advantages of the present method.