Standard-Error Estimates for Rates of Change From Indirect Measurements

Abstract

When indirect measurements are used to obtain rate-of-change data, an additional source of uncertainty is introduced that must be taken into account in the mean-rate and standard-error estimates. A procedure to account for this uncertainty is described. The chain rule of differentiation is used to decompose the rate into the product of calibration and primary experiment parts. Mean-rate and standard-error estimates are then obtained in terms of the component means and standard errors. The procedure is demonstrated by an analysis of some fatigue-crack-growth data.

KEY WORDS:

• Calibration
• Error-in-variables
• Error propagation
• Fatigue
• Variance components