Application of Non-Linear Least Squares Procedures to Power Functions and Upper limit Curves,

摘要

A non-linear least squares procedure for estimating mean power function curves is presented in this report. Prediction and tolerance upper limit curve expressions are derived by analogy with standard least squares methods. A chart of minimum widths for tolerance upper limit curves is given in this report. Data points used in the non-linear least squares procedure are checked for outliers and deficiencies to prevent distortions in calculated power functions and upper limit curves. The non-linear least squares method is compared with the standard least squares procedure for obtaining power function coefficient estimates and upper limit curves. For NATF (Naval Air Test Facility) applications the non-linear least squares procedure gives more consistant coefficient estimates than the standard method. Upper limit curves of the non-linear least squares procedure generally have smaller widths than standard method upper limit curves for large independent variable values. Sharper confidence bound definitions are therefore provided with the non-linear least squares procedure for critically important high independent variable values. It is shown in the report that non-linear least squares upper limit curves are in close agreement with exact upper limit curves of the straight line model. (Author)