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1
Drawing StatisticalInference from
Simulation Runs...
...the "fun" stuff!
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Essential Issues
Warm-up Period
Replication Determination
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THENONTERMINATING
SIMULATION
THENONTERMINATING
SIMULATION
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Warm-up Period
Initial transient period.
When steady state is achieved
Determines deletion amount
Graphical procedure
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Definitions
W = Warm-up (transient) period
L = Length of replication
n = Number of replications
m = Moving average period
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Procedure
Select decision variable. (e.g. Quantity of WIP)
Make n>4 replications of duration L, where L is much larger than expected value of the transient period.
Prepare a table of observations.
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Procedure Calculate the average across each of the n periods (e.g. all day 1s, all day 2s, etc.).
Plot a moving average for m = 5, m = 10 or m = 15.
Select the warm-up period W that shows the smallest deviation from a straight line average.
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Daily Number in WIP
Rep 1 Rep 2 Rep 3 Rep n DailyAvg *
Day 1
Day 2
Day 3
Day 30
* Averages are hypothetical assuming all observations are considered.
etc.
104 112 106.3
83 96 89.2
101
89
100 94 88 96.4
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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
DailyAvg
MovingAvg
10
125
100
75
1 30Periods (days)Moving Average m = 5
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125
100
75
1 30
Periods (days)Moving Average m = 10
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Convergence
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Clues to Success Use n > 4 replications initially.
Keep m > L/2.
Increase replications n rather than length of run L to achieve greater smoothness.
Better to choose a warm-up period too long than too short.
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THE TERMINATINGSIMULATION
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How Many Replications
10 ?
50 ?
100 ?
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A “Quick” Method
Select your decision variable. (e.g. Average process time)
Decide how close you would like to be.
“I’d like to be within +/-3 minutesof the actual process time…”“I’d like to be within +/-3 minutesof the actual process time…”
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A “Quick” Method
“Estimate” the standard deviation of your decision variable...
“I believe the maximum and minimum processtimes are 65 and 15 minutes respectively.”
“I believe the maximum and minimum processtimes are 65 and 15 minutes respectively.”
65 - 15 = 50
S = 50/6 = 8.33
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A “Quick” Method
Select precision level.
“I want to be 95% certain of myanswer” (i.e. a = .05). “I want to be 95% certain of myanswer” (i.e. a = .05).
For 95% confidence interval, Z = 1.96.
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A “Quick” Method
Solve...
n = ( )Z * S
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n = ( 1.96 * 8.33 )2
2
n = 31
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Precision Level Differences
How Close 90% 95% 99%to Actual Mean (Min)
0.5
3.0
10.0
747 1066 1848
21 30 51
2 3 5
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OrUse Stat::Fit
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Open Stat::Fit from the Tools menuOpen Stat::Fit from the Tools menu
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Use the Utilities -Replicationsmenu and fill-inthe informationas we did in thepreviousexample
Use the Utilities -Replicationsmenu and fill-inthe informationas we did in thepreviousexample
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Number ofreplicationsNumber ofreplications
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