---
title: "Initial bias and its elimination"
subject: "Simulation and Modeling"
chapter: 8
key: "semester_8/simulation_and_modeling:initial-bias-elimination"
source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/initial-bias-elimination
site: BCT Engineering
---

# Initial bias and its elimination

Simulation and Modeling · Chapter 8: Analysis of simulation output

- Asked in: 2072 Ashwin, 5 marks; 2072 Magh, 5 marks; 2070 Bhadra, 5 marks; 2070 Magh, 5 marks (asked 4 times)
- Video: [Simulation- 7: Analysis of simulation output  | Chapter 7| csit 5thsem #5thsem](https://www.youtube.com/watch?v=-UyrKZUIAyk) — GYAN WALLA
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/initial-bias-elimination
- Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-8

## Question

What is initial bias? Explain the methods / approach for the elimination of initial bias in analysis of simulation output.

## Short answer

Initial bias is the error from starting conditions that do not represent steady state. Methods to remove it include intelligent initialization to a typical state, deleting a warm-up period (chosen by Welch's graphical method), making runs very long, and using replication with deletion of initial observations.

## Answer

**Initial bias** (initialization bias, start-up problem) is the error in the estimated steady-state measures caused by the artificial starting conditions of a simulation run. A run usually starts "empty and idle", which is unlike the long-run behaviour of the system, so the early observations are not representative of steady state and pull the average away from the true value.

For example, a bank simulation starting with no customers shows short waiting times during the first hour. Including these data underestimates the true mean waiting time.

#### Methods to reduce or remove initial bias
1. **Intelligent initialization**: start the model in a state that is typical of steady state, such as with the average number of customers already in the queue. The state can be taken from the real system or from a pilot run.
2. **Deletion of initial data (warm-up period)**: run the simulation for a warm-up time T0, discard all observations collected before T0, and compute the statistics only from the remaining data. For a run of length TE, the estimate is the average over (T0, TE].
3. **Long runs**: make the run so long that the initial transient has little effect on the overall average. This is simple but costly.
4. **Replication with deletion**: make R independent replications, delete the first d observations of each, and average the rest.
5. **Batch means**: divide one long run into equal batches after deleting the warm-up, and use batch averages as nearly independent observations.

#### Choosing the deletion point: Welch's method
1. Make R (at least 5) replications of length m, and compute the average Y_j over replications for each observation index j.
2. Smooth the averaged series with a moving average of window w to remove noise.
3. Plot the smoothed series and find the point where it flattens.
4. Take that index as the number of observations to delete.

```text
 value
   |  .                  steady state
   |    .  ___ ___ ___ ___ ___ ___
   |     ./
   |  transient | 
   +------------+------------------> time
              T0 (delete before)
```
A warm-up that is too short leaves bias; one that is too long wastes data and raises the variance. In practice it is common to choose it generously.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is initial bias?
   A. Error in steady-state estimates caused by artificial starting conditions such as an empty and idle system
   B. Error from using too many replications
   C. Bias from a wrong random number generator
   D. Error in the t-table value
   Answer: A. Starting empty and idle makes early observations unrepresentative of steady state and biases the average. (Key point: Initial bias)

2. How does deletion of initial data (warm-up) work?
   A. Add extra observations at the start
   B. Discard observations before T0 and compute statistics from the remaining data
   C. Delete the last half of the run
   D. Restart the clock after each event
   Answer: B. Observations collected before warm-up time T0 are discarded, and statistics use only (T0, TE]. (Key point: Warm-up deletion)

3. In Welch's method, how is the deletion point chosen?
   A. By running one very short replication
   B. By the value of the t-statistic
   C. By choosing the largest observation
   D. By averaging over replications, smoothing with a moving average, and picking where the plot flattens
   Answer: D. Average across R replications, smooth, plot and take the point at which the series flattens. (Key point: Welch's method)

4. What is the effect of choosing too long a warm-up period?
   A. Bias increases
   B. It wastes data and raises variance
   C. Confidence intervals become invalid
   D. Nothing changes
   Answer: B. Too short leaves bias; too long discards useful data and increases variance. (Key point: Warm-up length)

## Related in Simulation and Modeling

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- [Simulation run statistics](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Asimulation-run-statistics) — Simulation and Modeling, chapter 8, asked 2×

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