Equilibrium Based Curve Fitting Method for Test Data With Nonuniform Variance

A recently developed equilibrium based curve/surface fitting method is extended to linear function with heteroscedastic data (variable variance). The concept of equilibrium weighted ‘force’ and ‘moment’ is proposed to derive curve fitting formulae, which are exactly the same as that obtained with the traditional weighted least squares (LS) method for a linear function. Furthermore, a system of four equations, i.e., a “force” equilibrium equation, a “moment” equilibrium equation, a “equivalency” equation, and a “moment balance” equation have been established to solve both mean curve and the standard deviation simultaneously. Finally, the application of these methods to data of fatigue and creep lives is presented.