Equilibrium Based Curve Fitting Method for Test Data With Nonuniform Variance

Abstract

A recently developed equilibrium based curve/surface fitting method is extended to linear function with heteroscedastic data (variable variance). The concept of equilibrium weighted “forceâ€‌ and “momentâ€‌ 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 “forceâ€‌ equilibrium equation, a “momentâ€‌ equilibrium equation, an “equivalencyâ€‌ equation, and a “moment balanceâ€‌ 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.