Imagine two factories that run under identical random rules—machines break and repair at the same rates—but one factory starts with more working machines. Will it tend to stay ahead, even years later? In this chapter we build a clever joint construction, called a coupling, that lets us run the two systems side by side on the same randomness, keeping their order intact at every moment. Once we have that, we can prove that the stochastic order between their state distributions is preserved forever.