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Case Study - Car Trip and Risk

Case Study - Car Trip and Risk. Trip Data 1,000 miles Probability of flat tire: Average of 1 flat tire per 1,000 miles Service stations every 100 miles What is the probability of successfully completing the trip for each of the following scenarios :

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Case Study - Car Trip and Risk

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  1. Case Study - Car Trip and Risk • Trip Data • 1,000 miles • Probability of flat tire: Average of 1 flat tire per 1,000 miles • Service stations every 100 miles • What is the probability of successfully completing the trip for each of the following scenarios: • Scenario 1 - Driver #1 - high risk taker: no spare tire • Scenario 2 - Driver # 2 - time is money: spare; but, does not stop to repair flat • Scenario 3 - Driver # 3 - good risk manager : spare & repairs flat tire ASAP • Speed Limits • Stages 1, 4, 5, 8, 10: 40 mph • Stages 2, 3, 6, 7, 9 : 60 mph • Is Problem adequately specified? • Important to critically assess data • Is all the information available? ENGR 202 Lab 1

  2. Questions • What is the probability of completing the trip without help? • How many flat tires do you expect? • How long should it take to complete the trip? ENGR 202 Lab 1

  3. How Good Is Your Intuition? • Assume you can drive at the speed limit and no car failures • What is the average speed? • How long will the trip take? • How many flat tires can you expect? • If you have a spare and fix flat ASAP, are you guaranteed to successfully complete trip? • What are the best and worse times for each driver? • How would you rank the risks for each driver? ENGR 202 Lab 1

  4. Additional Necessary Data • Estimation of Potential Delays - Expert opinion ENGR 202 Lab 1

  5. How To Solve Problem? • Common sense • Expert Opinion • Monte Carlo simulation using Excel ENGR 202 Lab 1

  6. Common Sense Solution • 1.0 Best time with no speed violation • 1.1 Assume no flat tire • Min Time, hr: 20.83 • 1.2 Assume 1 flat tire • Driver 1 : 22.83 hrs Optimistic - 2 hrs for repair • Driver 2 : 21.17 hrs 1/3 hr to replace flat • Driver 3 : 21.83 hrs 1 hr to replace & repair flat • Typical PM: I can do trip in 22 hrs; I have slack of 1 hour • What is the PM’s probability of success? • Use Monte Carlo simulation ENGR 202 Lab 1

  7. Monte Carlo Simulation • Developed during Manhattan Project in 1940’s • Each uncertain input parameter is modeled as random variable using a probability distribution for outcome Vs. probability • Run computational model multiple times with each input sampled according to its distribution • Analysis shows the distribution of possible outcomes • Many commercial packages available as add-ins to standard spreadsheets such as Excel • @Risk, Crystal Ball, SIM.xla • Gaining popularity in diverse area • logistics, risk management, decision analysis, marketing, strategy • Basic steps • Build a model of the uncertain situation • Specify the distribution functions • Run the simulation and analyze the results ENGR 202 Lab 1

  8. What Are Random Numbers? • Random numbers (RN)= Uncertain numbers • Usually interested in RNs that satisfy well-known idealized distributions • uniform, discrete, poisson, triangular,…. • Distributions have statistical properties such as mean, mode, median, standard deviation,… • Representation of distributions • Curves, histograms, tables • Cumulative distribution • Prob(random variable X <= a) • Prob(random variable X <= max) =1 ENGR 202 Lab 1

  9. How To Generate Random Numbers • How can one generate random integers uniformly distributed between 1 and 51? • Mechanical spinning wheel, 51 pieces of papers, software,... • Rand() in Excel generates #’s between 0 and 1 from a uniform distribution • But, we are interested in simulating random numbers having a specified distribution • Many techniques available • But, there are easier ways than programming yourself • Many PC tools available: SIM.xla, @Risk, Cristal Ball,… • Understand the difference between the statistical distribution functions and the RN generating functions ENGR 202 Lab 1

  10. Car Trip - Lessons Learned • Understand the limitations of any model & assumptions • FR independent of trip distance • All tires are good at start • Tires fail independently; no common cause failures • How would the scenario be changed if part of the road is extremely bad? • Monte Carlo simulation captures the uncertainty aspects of the problem • MC captures the possible outcomes • MC averages are consistent with the closed form solutions, if possible • MC provides additional information about shape or distribution of outcomes • More general; but, requires more numerical modeling and computations • Excel is a powerful analysis tool when used properly! ENGR 202 Lab 1

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