Arriving Within Tolerance: Transit Success Probability Under Advance-Rate Dispersion

A transit that aims at a phase and arrives at a neighbouring one has not failed loudly; it has failed by a small angle, which is worse. This paper computes the probability of arriving within tolerance when the advance rate varies across a payload. With a Gaussian fractional dispersion s in the advance rate, the arrival phase error after one turn has standard deviation 2 pi s, and the probability of landing within the 0.0667 rad tolerance is 1.0000 at s = 0.1 percent, 0.7116 at s = 1 percent, and 0.1681 at s = 5 percent. Reaching a 99 percent success probability requires the dispersion to be held at or below 0.412 percent. Rate uniformity, not mean rate accuracy, is the binding specification for reliable transit: a drive can be recalibrated for a wrong mean, but dispersion cannot be calibrated away. Computed from stated assumptions; not measured. SIMULATED, NOT MEASURED.