Estimating the Correlation between Destructively Measured Variables using Proof-loading

Two simple proof-load testing procedures are suggested to estimate the correlation between two variables that can individually only be determined destructively. The first procedure assumes that the means and variances of the variables are known. The second testing procedure is more flexible and requires no prior information. By assuming that the variables have a bivariate normal distribution and considering only the number of units that fail at each proof-load, we determine the maximum likelihood estimate for the correlation coefficient. Theoretical and simulation results compare favorably with previously suggested more complicated procedures, and guide the practitioner in appropriate choices for the proof-load levels.