0

When observing the output of a system simulation, how does one arrive at a reasonable number of observations needed to make an inference about that system?

I am observing widgets flowing through a manufacturing system and observing their wait times in queue and the queue length. The system is not modeled with an equation and distributions of observations are unknown. Ideally, one would like to be infer a distribution. If it were normal, then it would be helpful to estimate the mean & standard deviation from the 'sample' (observations). This begs the question, how many samples (model replications) will be performed.

gatorback
  • 101
  • 1
    Depends entirely on the specifics, which have been entirely omitted from your question.:) What is being simulated? You mention no probability or statistics in the question, but use the hashtag of "statistical inference." The less you tell, the less response you will get. – avs Aug 19 '16 at 22:34
  • 2
    This may be relevant: https://en.wikipedia.org/wiki/Sample_size_determination – NoChance Aug 19 '16 at 22:40
  • 1
    Two issues govern: (1) What is the variability of the process? If it always gives the same result, then $n=1$ observation suffices. If extremely variable, then you need a bigger $n$. (2) How accurate does your estimate have to be? For example, if your main job to to estimate the mean $\mu$ of a normal distribution, then a 95% confidence interval is $\bar X \pm 1.96\sigma/\sqrt{n},$ where the pop SD $\sigma$ may need to be estimated by the sample SD $S$ and the formula for the CI becomes just a little messier. Roughly, 4 times as many observations cuts the length of the CI in half. – BruceET Aug 20 '16 at 06:16
  • 1
    If your problem really deals with waiting times, they are not likely to be normal. They are often modeled by the exponential distribution. In that case it is enough to use $\bar X$ which estimates both the mean and the SD of the exponential distribution. But you will need to use the chi-squared distribution (equivalently a gamma dist'n) to get a CI for $\mu.$ Wikipedia's article on exponential distribution has details. – BruceET Aug 20 '16 at 06:28

0 Answers0