Can anyone suggest a way to run "Fit Life by X" when the form is
mu (log lifetime) = beta0 + X^(beta1)?
From running the reciprocal and custom relations, beta1 values between -1 and -2 seems to give the best fit to the observed failure times.
You cannot. Fit Life by X assumes the formula for mu is linear in beta's. I don't see whether this model has an equivalent form which is linear in beta's. I would suggest using Nonlinear to solve the problem.
The Nonlinear Model platform seems to work well. Carrying this beyond the original question, it looks as though I would need to create a 'dummy' X variable in order to combine two factors, e.g. Peck's Power-law humidity model.