4.8: Summary
- Page ID
- 30974
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This chapter discusses the design and analysis of simulation experiments. Elements are defined and organized into a design. A method to construct statistically independent observations to avoid correlation difficulties is described.
The need to gather evidence that a model is valid and verified is presented. Possible strategies in this regard are given. Ways to compare scenarios, both through statistical analysis and the examination of data, are discussed.
Problems (Similar problems are associated with each of the case studies for further practice).
- Suppose 4 scenarios were compared in a pair-wise fashion with respect to one performance measure. How many comparisons are made? If \(\ \alpha\) = 0.01 is used for all comparisons, what is the upper bound on the \(\ \alpha\) for all the comparisons made? What if \(\ \alpha\) = 0.05 is used? Which of the two values for \(\ \alpha\) should be used?
- Consider the following table of simulation results.
Replicate Workstation % Busy Time – Scenario One Workstation % Busy Time – Scenario Two 1 87 78 2 80 72 3 79 71 4 80 72 5 78 71 - Construct 95% confidence intervals for the workstation % busy time for each scenario.
- Construct a paired-t confidence interval, \(\ \alpha\) = 0.05, to compare the percent busy time of a workstation for two scenarios.
- Consider the following table of simulation results.
Replicate Maximum Time – Scenario One Maximum Time – Scenario Two 1 241.8 122.0 2 61.1 62.6 3 122.1 94.7 4 111.6 73.1 5 154.4 105.2 - Construct 95% confidence intervals for the maximum time for each scenario
- Construct a paired-t confidence interval, \(\ \alpha\) = 0.05, to compare the maximum time at the workstation for the two scenarios.
- Are the confidence intervals constructed in a. and b. approximate or exact? Defend your answer.
- Develop the design of a terminating simulation experiment for problem 2-10.
- Defend the use of approximate confidence intervals.
- Consider the simulation of a single workstation consisting of a single machine with an operation time uniformly distributed between 5 and 10 minutes. The time between part arrivals is exponentially distributed with a mean of 9 minutes.
- What verification evidence could be sought?
- What validation evidence could be sought?
- Conduct a complete analysis of a simulation experiment regarding a single workstation with one machine based on the data that follow. The mean time between arrivals is 10 minutes and the operation time is 8 minutes. The simulation was run for 168 hours. Management wishes to achieve a production quota of 1000 items per 168 hours.
- Provide evidence for the verification and validation of the simulation based only on the data in the following table and the problem statement.
Replicate Workstation % Busy Tim Number of Entities Arriving Number of Entities Departing Number of Entities in Processing at the End of the Simulation Number of Entities in the Buffer at the End of the Simulation 1 87 1044 1044 0 0 2 80 961 960 1 0 3 79 944 943 1 0 4 80 965 959 1 5 5 78 942 942 0 0 - Compare the two scenarios using first the average number in the buffer and then the maximum as described below. Use only the data that follows and items i-iv.
- Compute appropriate statistical summaries (average, standard deviation, minimum, maximum, range, and confidence intervals) and state any evidence found from this information.
- Compute and display appropriate histograms and state any evidence seen in them.
- In how many replicates is the new case better than the current operations? What evidence does this information provide?
- Perform the appropriate statistical analysis to compare the scenarios.
Number in Buffer Current Operations New Case Replicate Average Maximum Average Maximum 1 12.8 28 4.3 15 2 1.2 8 1.1 7 3 4.3 16 2.6 16 4 2.9 10 1.9 8 5 3.6 17 2.1 12 6 3.7 10 2.0 8 7 2.1 12 1.2 7 8 3.5 17 1.6 11 9 2.7 13 1.4 9 10 2.0 10 1.2 9 11 1.4 8 1.3 10 12 2.0 12 1.4 10 13 1.4 7 1.4 9 14 2.7 17 2.0 12 15 1.7 16 1.2 9 16 1.5 7 0.9 8 17 5.2 26 4.2 17 18 3.2 15 2.0 9 19 3.1 14 2.0 9 20 2.2 11 1.2 8
- Provide evidence for the verification and validation of the simulation based only on the data in the following table and the problem statement.