Probability of fatigue failure and minimum sample size requirements for cyclically loaded bone

Abstract

Fatigue-life measurements of bone exhibit a significant amount of scatter, which may be characterized probabilistically using a Weibull analysis. Despite an abundance of fatigue testing literature, a standard recommendation for the number of samples required to adequately characterize the probability of fatigue failure in bone does not exist. The primary objective of this work was to determine the minimum sample size required to fit a Weibull distribution to fatigue-life measurements of cyclically loaded bone. Two existing experimental datasets comprising cortical and subchondral bone samples were used in this work. Weibull parameters were estimated using both the maximum likelihood and rank regression methods. A Monte Carlo simulation was used to estimate Weibull parameters for different sample sizes and a convergence analysis was used to determine the minimum required sample size. A simulated dataset with known population parameters was also used to assess the accuracy of the estimated Weibull parameters and to compare the two estimation methods. Our findings suggest that as many as n = 11 samples may be required to adequately quantify Weibull parameters from fatigue tests of bone. At the converged sample size, Weibull parameters differed from true population-level parameters by 3 %–25 %, depending on the estimation method. The maximum likelihood method provided the most accurate and precise estimates of Weibull parameters. These findings provide a framework for future studies aimed at reliably quantifying the probability of fatigue failure in bone.