A Theory for the Mortality Curve of Filament Lamps

We demonstrate for the first time that the ejection of tungsten atoms from a hot filament can be modeled by a binomial distribution. The relevant ejection chance per atom may have an arbitrary temporal profile depending on the presence of uniform Richardson evaporation, hot spots and temperature variation along the wire. A normal approximation is made and the lamp is supposed to fail if the undecayed atomic fraction drops below a critical value. The resulting formula for the lamp’s survival probability in terms of error function has one free parameter and is shown to be in excellent agreement with the experimental mortality curve.