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Modeling and simulation in engineering

Overview

Mehmet Sahinoglu

Published Online: Apr 19 2013

DOI: 10.1002/wics.1254

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Abstract This review article will explore the innovative and popular theme of engineering modeling and simulation, predominantly in the manufacturing industry and cybersecurity world, citing severe challenges, advantages and time‐ and budget saving solutions and its future. The power of simulation is not an exaggeration but an understatement. The favorable outcomes since the advent of digital computers and software revolution could not have been achieved, especially without the multiple benefits of statistical simulation, which underlies the widespread use of modeling and simulation in engineering and sciences, stretching from A (Astronomy) to Z (Zoology). This refers not only to research findings in verifying a certain piece of theory, such as that of the recently discovered Higgs Boson, but in testing new products to innovate new discoveries so as to make our universe a more peaceful place by modeling and simulating the future projects and taking precautions before disasters occur. The review explores a cross section of engineering modeling and simulation practices illustrating a window of numerical examples. WIREs Comput Stat 2013, 5:239–266. doi: 10.1002/wics.1254 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Algorithms and Computational Methods > Random Number Generation Statistical Models > Simulation Models

Given the input table, the p.d.f. of the two‐state SL is plotted for UP (r) and DOWN (q) for 90% confidence analytically showing mode (m), mean (E) with upper & lower confidence bounds.

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Computer modeling and interplay between experiments, simulation, and theory.25

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Uniform numbers testing; Ho: random versus Ha: not random for 250,000 runs. Ho is not rejected. After 40 cycles × 250K = 10,000K = 10,000,000 simulations there is still no reject Ho = Random Sequence. This may signal still no rejection of random sequence from the earlier safe threshold: 50K simulations for a JAVA coding uniform random number generator. Important Note: In this figure, buttons indicate: No of values = 250,000 (simulation runs), DF = 6 (Section on Generic Theory, by Knuth's Technique10,11), Significance level (Type‐I error) = 5%, Total Runs: 41,606 ×1 + 51,836 ×2 + 23,059 ×3 + 6583 ×4 + 1482 ×5 + 290 ×6.093 (average for >6) = 250,000, where bold numbers from 1 to >6 are calculated run sizes by Knuth's method. χ² calculated = 7.57 <χ² critical value = 12.59. Do NOT reject Ho: random sequence.

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Uniform numbers testing; Ho: random versus Ha: not random for 100,000 runs. Ho is NOT rejected. After 50 cycles × 100K = 5000K = 5,000,000 simulations, there is still no reject Ho = random sequence. This may signal still no rejection of random sequence from the earlier safe threshold: 50K for a JAVA coding uniform random number generator.

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Uniform numbers testing; Ho: random versus Ha: not random for 50,000 runs. Ho is NOT rejected. After 60 cycles × 50K = 3000K = 3,000,000 simulations there is still no reject Ho = random sequence. This may signal a cut‐off point of no rejection of random sequence from this point on. Safe threshold may be 50K for JAVA coding uniform random number generator.

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Uniform numbers testing; Ho: random versus Ha: not random for 10,000 runs. Ho is rejected. On the average, one out of 25 cycles of 10,000 = 250,000 simulations will end up rejecting Ho: random.

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Uniform numbers testing; Ho: random versus Ha: not random for 10000 runs. Ho is NOT rejected.

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Uniform numbers testing; Ho: random versus Ha: not random for 5000 runs. Ho is rejected. On the average, one out of 10 cycles of 5000 = 50,000 simulations will end up rejecting Ho: random.

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Uniform numbers testing; Ho: random versus Ha: not random for 5000 runs. Ho is NOT rejected.

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Uniform numbers testing; Ho: random versus Ha: not random for 500 runs. Ho is rejected. On the average, one out of 40 cycles of 500 runs = 20,000 simulations will end up rejecting Ho: random.

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Uniform numbers testing; Ho: random versus Ha: not random for 500 runs. Ho is not rejected.

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Monte Carlo simulations for the cyber server ($8000 asset) example with inputs in Table 8.

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The Monte Carlo (MC) simulation results of the 2 × 2 × 2 security meter sampling design.

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DES results of the 2 × 2 × 2 security meter sampling design.

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Simplest 2 × 2 × 2 tree diagram for two threats and for two vulnerabilities in a cyber‐risk scenario.

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Complex network of seven units with input data, where source: s = 1 and target: t = 7.

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Given the input table on the l.h.s. column, the p.d.f.s of the three states are plotted for UP (r), DER (d), and DOWN (q) for a 90% confidence level showing mode (m), mean (E) with upper & lower confidence as centrality measures for n = 100,000 simulation runs.

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Simple series system of two units.

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Relationships for distributions in statistical simulation where α₁ = α₂ or α₁≠α₂, and L = (β₁/β₂) for SL (α, β, L). (Dashed arrows indicate ‐→∝ Reprinted with permission from Ref 20 Copyright 2007, Wiley & Sons, Inc)

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Similar to Figure 12 but with Median (M), first and third quartiles as location measures for n = 100,000 simulation runs plotted for UP (r), DER (d), and DOWN (q).

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The input data in Table 1, and simulation results in Tables 2–4 and Figures 5–7 display the cumulative reliability plots of the three states for UP (r), DER (d), and DOWN (q).

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P(DOWN) Cumulative reliability plot with 10,000 Monte Carlo simulation runs.

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P(DER) Cumulative reliability plot with 10,000 Monte Carlo simulation runs.

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P(UP) Cumulative reliability plot with 10,000 Monte Carlo simulation runs.

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A sample illustration of feasible transitions from Figure 3 implemented to subsections of Three‐State Sahinoglu Probability Model of Production Units (Monte Carlo Simulation).

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Three‐state Markov diagram of a repairable hardware unit with UP, DOWN and DER states.

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