# Error Propagation Calculation

I have a few machines that are used to calibrate each other.

Machine 1 has is accurate to 0.025%

Machine 1 is used to calibrate Machine 2, which has an accuracy of 0.005%

Machine 2 is used to calibrate Machine 3, which has an accuracy of 0.025%

Machine 3 is used to calibrate Machine 4, which has an accuracy of 0.04%

Using the root of the sum of the squares gives an error for Machine 4 of just over 0.052%, but I need it to be below 0.05%. Is there any games I can play (like bootstrapping, maybe) to get this error down?

In other words, I can get all sorts of empirical calibration trials...Can I use that data somehow to bring down that error propagation?

• machine 1 has worse accuracy than Machine 2, yet it's used to calibrate the latter? – Aksakal Apr 9 '14 at 13:56
• Yes. I don't like it either, but it's a matter of cost and size (machine 2 needs almost a crane to move, so sending it to be calibrated at a measurement facility is unfeasible). Machine 1 can fit in a suitcase, and therefore is what is sent out to be calibrated at a measurement facility. – testname123 Apr 9 '14 at 13:58
• What's your data? is it measurements from Machine 5? – Aksakal Apr 9 '14 at 14:08
• Yes...i can get measurement data from all machines – testname123 Apr 9 '14 at 14:10
• Then why do you have to measure with Machine 4? Why not measure it all with Machine 2? I think I'm missing something in your setup – Aksakal Apr 9 '14 at 14:12

Machine 4's precision is going to be 0.04% no matter what. Its accuracy is going to be $\sqrt{0.025\%^2+0.005\%^2+0.025\%^2}=0.036\%$.