5 3σ Protocol

5 3σ Protocol A stable equilibrium formula in the context of a mean can be described using a differential equation. Let the state of a system be described by x(t), and its rate of change be given by the function f(x). The governing equation is: dx/dt = f(x). An equilibrium point, which represents the mean state x̄ the system will settle into, is a point where the rate of change is zero. The formula to find an equilibrium point x̄ is: f(x̄) = 0. For this equilibrium point x̄ to be stable, any small disturbance must cause the system to return to x̄. This condition is met when the first derivative of the function f(x), evaluated at the equilibrium point x̄, is negative. The formula for a stable equilibrium is: f'(x̄) = df/dx|x=x̄ < 0. This negative derivative ensures that if the system's state x moves slightly away from x̄, the "force" or rate of change will push it back toward the mean.