This document discusses output analysis for simulation models and eliminating initial bias. It explains that initializing a simulation with an empty or idle state can cause initialization bias, skewing early results. Two common approaches to address this are to start simulations in a more representative state or remove an initial warmup phase of results. The ideal is to start from the true steady state distribution, while typically the warmup phase is eliminated by restarting after a pilot run determines how long the initial bias persists.

1. OUTPUT
ANALYSIS
FOR
SIMULATIO
MODELS
Eliminatio
of Initial
Bias:
Presented by
• Tilak Poudel

2. OUTPUT ANALYSIS FOR SIMULATION
MODELS
Introduction
• Output analysis focuses on the analysis of simulation results
(output statistics).
• It provides the main value-added of the simulation enterprise by
trying to understand system behavior and generate predictions
for it.

3. TYPES OF SIMULATION WITH REGARD
TO OUTPUT ANALYSIS
Simulation
Non Terminating
Simulation
Steady state Cycle
parameters
Steady state
parameters
Terminating
Simulation

4. ELIMINATION OF INITIAL BIAS
• Initialization bias: It is condition to choose initial values for the
state variables that are not representative of the steady state
distribution.

5. INITIALIAZATION BIAS
• Example: let's say that you're modeling a factory making washing machines. When your
simulation starts, the simplest initial state is for the factory to have no work-in-progress -
that is, the factory has no washing machine parts in any part of the process. As the
simulation runs, you introduce parts, which progress through the simulation until
completed washing machines are shipped.
• Let's say that you count the number of washing machines shipped by the simulation. You
can then estimate the mean number of washing machines shipped per hour as follows:
• mean hourly throughput = (number of washing machines shipped) / (simulation time in
hours)
• But, we're going to see an initialization bias, because it takes time for the simulation to
complete the first washing machine; we might not ship any washing machines for some
time.

6. ELIMINATION OF INITIAL BIAS
• Divide the simulation into two phases, warm-up phase and
steady state phase.
• Data collection doesn't start until the simulation passes the
warm-up phase.

7. ELIMINATION OF INITIAL BIAS
Warmupphase
steady state phase

8. ELIMINATION OF INITIAL
BIAS
Two general approaches can be taken into remove the bias.
1. The system can be started in a more representative then an
empty state.
2. The first part of the simulation can be removed.

9. ELIMINATION OF INITIAL BIAS
• The ideal situation is to know the steady state
distribution for the system, and select the initial
condition from that distribution.
• The more common approach to remove initial bias is to
illuminate an initial section of run.

10. ELIMINATION OF INITIAL BIAS
• The run is started form an idle state and stopped after a certain
period of time.
• The entities existing in that system at that time are left as they
are.
• The run is then restarted with the statistics being gathered from
the point of restart.

11. ELIMINATION OF INITIAL BIAS
• No simple rules can be given to decide how long an interval
would be eliminated.
• It is advisable to use some pilot runs starting form idle state to
judge how long the initial bias remains.

12. TRANSIENT
AND
STEADY-
STATE
BEHAVIOR
• Transient State : It is the output process for the initial condition
I , at discrete time i .
• It shows the density of random variable Y vary from one
replication to another.
• Steady state: It shows the distribution of the random variable
from a particular point will be approximately same as each
other.
• It does not depend on initial conditions .

13. TRANSIENT AND STEADY-STATE
BEHAVIOUR

14. Q & A
Dilemma …???
Queries are Welcomed…..!! 

15. Thank YOU……..