1. 191 Drawing Statistical Inference from Simulation Runs......the "fun" stuff!

2. 192 Essential Issues u Warm-up Period u Replication Determination

3. 193 THE NONTERMINATING SIMULATION THE NONTERMINATING SIMULATION

4. 194 Warm-up Period u Initial transient period. u When steady state is achieved u Determines deletion amount u Graphical procedure

5. 195 Definitions W = Warm-up (transient) period L = Length of replication n = Number of replications m = Moving average period

6. 196 Procedure u Select decision variable. (e.g. Quantity of WIP) u Make n>4 replications of duration L, where L is much larger than expected value of the transient period. u Prepare a table of observations.

7. 197 Procedure u Calculate the average across each of the n periods (e.g. all day 1s, all day 2s, etc.). u Plot a moving average for m = 5, m = 10 or m = 15. u Select the warm-up period W that shows the smallest deviation from a straight line average.

8. 198 Daily Number in WIP Rep 1 Rep 2 Rep 3 Rep n Daily Avg * Day 1 Day 2 Day 3 Day 30 * Averages are hypothetical assuming all observations are considered. etc. 104112106.3 839689.2 101 89 100948896.4

9. 199 106.3 89.2 96.4 101.6 110.6 99.4 116.3 121.5 97.7 101.1 112.6 102 106.3 97.3 100.8 103.1 104.5 104.9 104.5 Daily Avg Moving Avg

10. 200 125 100 75 130 Periods (days) Moving Average m = 5

11. 201 125 100 75 130 Periods (days) Moving Average m = 10 15 Convergence

12. 202 Clues to Success u Use n > 4 replications initially. u Keep m > L/2. u Increase replications n rather than length of run L to achieve greater smoothness. u Better to choose a warm-up period too long than too short.

13. 203 THE TERMINATING SIMULATION

14. 204 How Many Replications 10 ? 50 ? 100 ?

15. 205 A “Quick” Method u Select your decision variable. (e.g. Average process time) u Decide how close you would like to be. “I’d like to be within +/-3 minutes of the actual process time…” “I’d like to be within +/-3 minutes of the actual process time…”

16. 206 A “Quick” Method u “Estimate” the standard deviation of your decision variable... “I believe the maximum and minimum process times are 65 and 15 minutes respectively.” “I believe the maximum and minimum process times are 65 and 15 minutes respectively.” 65 - 15 = 50 S = 50/6 = 8.33

17. 207 A “Quick” Method u Select precision level. “I want to be 95% certain of my answer” (i.e. a =.05). “I want to be 95% certain of my answer” (i.e. a =.05). For 95% confidence interval, Z = 1.96.

18. 208 A “Quick” Method u Solve... n = ( ) Z * S 3 n = ( 1.96 * 8.33 ) 2 2 n = 31 3

19. 209 Precision Level Differences How Close 90% 95% 99% to Actual Mean (Min) 0.5 3.0 10.0 74710661848 213051 2 35

20. 210 Or Use Stat::Fit

21. 211 Open Stat::Fit from the Tools menu Open Stat::Fit from the Tools menu

22. 212 Use the Utilities - Replications menu and fill-in the information as we did in the previous example Use the Utilities - Replications menu and fill-in the information as we did in the previous example

23. 213 Number of replications Number of replications

24. 214

25. 215

26. 216