Darts and Process Tampering
Larger values of n make it easier to see how the different tampering rules affect the process over time.
We use a function normalSample(t2) that shoots a dart aiming at the point
t2 on a vertical wall. Each shot is chosen from a normal distribution
with mean t2 and standard deviation σ.
By default the standard deviation is σ = 0.02 and the number of shots per experiment is n = 15, but you may change these values before starting the experiments. In this run the app is using σ = 0.020 and n = 15. Larger values of n make it easier to see the long–run effects of tampering.
Our target will be the value 1 on the wall. We will have n shots in each of three experiments.
Experiment 1 (no help).
We fix the aim at t2 = 1 and call normalSample(1)
n times. This produces landing positions
x1, x2, …, xn.
We do not adjust anything between shots.
Experiment 2 (adjusting from the last aim).
We again start with t2 = 1. After each shot yk we compute
its error from the target, yk − 1, and then we move the aim
from its current position by that amount in the opposite direction:
t2_new = t2_old − (y_k − 1).
This is the classic “over–control” rule: we keep chasing the last shot from wherever
we were aiming.
Experiment 3 (adjusting from the original target).
Now, after each shot zk we again look at the error zk − 1, but
we place the new aim the same distance from the original target 1, on the
opposite side:
t2_new = 1 − (z_k − 1) = 2 − z_k.
So if a dart lands 0.0277 above the target at 1.0277, the new aim is 0.9723,
which is 0.0277 below the target.
In the app, the computer performs these adjustments and tells you what it is doing. Your job is to keep pressing the button and watch how the patterns of darts change from Experiment 1 to 2 to 3.
At the end we plot the n darts from all three experiments on the same graph and compare their sample means and variances.