A new,reliable,and simple-to-use method for the analysis of a population of values of a random variable using the Weibull probability distribution: Application to acrylic bone cement fatigue results

Abstract

In cases where the Weibull probability distribution is being investigated as a possible fit to experimentally obtained results of a random variable (V), there is, currently, no accurate and reliable but simple-to-use method available for simultaneously (a) establishing if the fit is of the two- or three-parameter variant of the distribution, and/or (b) estimating the minimum value of the variable (V₀), in cases where the three-parameter variant is shown to be applicable. In the present work, the details of such a method – which uses a simple nonlinear regression analysis – are presented, together with results of its use when applied to 4 sets of number-of-cycles-to-fracture results from fatigue tests, performed in our laboratory, using specimens fabricated from 3 different acrylic bone cement formulations. The key result of the method is that the two- or three-parameter variant of the probability distribution is applicable if the estimate of V₀ obtained is less than or greater than zero, respectively.