Strategy 1 : Requires no adjustment.
This strategy assumes the cannon is aimed
correctly and any deviation is due to random variation in the process.
This strategy always aims the cannon at 0, no matter where the last
shot landed. This strategy is optimal (as you will hopefully show) for
stationary processes.
Example: To do this in the applet, first make sure the "Strategy 1" button is chosen and click "Reset". Type 0 in the "New Aim" box, and hit the "Fire" button. The value of where the cannonball hit will appear in the "Last Hit" box. I just did this and got -11.413, but for the next shot I aimed the cannon at 0. The next hit was 0.978, but for the next shot I aimed the cannon at 0. In fact, no matter where the cannonball hits, Strategy 1 continues to aim the cannon at 0.
Strategy 2 : This strategy changes the aim of the cannon by -y units (y is the location of the previous shot).
This strategy attempts to adjust the process after every
observation to compensate for perceived inaccuracy. The problem is,
for a stationary process the perceived inaccuracies are random, so
this strategy attempts to model noise, which cannot be done. You will
see the result.
Example: To do this in the applet, first make sure the "Strategy 2" button is chosen and click "Reset". The "Current Aim" box should contain 0.0. Type 0 in the "New Aim" box and fire the cannon. I just did and the cannonball landed at y= -27.429 (shown in the "Last Hit" box). Since the "Current Aim" is 0, for the next shot, I will aim the cannon at 0-y=0-(-27.429)=27.429. To do so, I enter 27.429 in the "New Aim" box and fire the cannon. This time the cannonball hit at y=27.029. Since the "Current Aim" is 27.4, I will aim the next shot at 27.4-y=27.4-27.029=.371.
Strategy 3 : This strategy aims the cannon at -y.
The rationale behind this strategy is that if the last observation
was 10 units too high, then to compensate, the cannon should be aimed 10 units
too low. You will see how successful this approach is for a stationary process.
Example: To do this in the applet, first make sure the "Strategy 3" button is chosen and click "Reset". The "Current Aim" box should contain 0.0. Type 0 in the "New Aim" box and fire the cannon. I just did and the cannonball landed at 0.845 (shown in the "Last Hit" box). For the next shot, I will aim the cannon at -y=-0.845. To do so, I enter -.845 in the "New Aim" box and fire the cannon. This time the cannonball hit at -1.939, so I will aim the next shot at -y=-(-1.939)=1.939.
Strategy 4 : This strategy aims the cannon at y, the location of the last shot.
This strategy attempts to attain uniformity by trying to make every result like the last one. For example, this is what might happen to the color of paint batches over time if the color of each new batch is matched to that of its predecessor. Will you want to buy paint from that company? Do the lab to find out!
Example: To do this in the applet, first make sure the "Strategy 4" button is chosen and click "Reset". The "Current Aim" box should contain 0.0. Type 0 in the "New Aim" box and fire the cannon. I just did and the cannonball landed at -4.203 (shown in the "Last Hit" box). For the next shot, I will aim the cannon at y=-4.203. To do so, I enter -4.203 in the "New Aim" box and fire the cannon. This time the cannonball hit at 19.559, so I will aim the next shot at 19.559.