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

Article type: Research Article

Authors: Janna, Sied | Dwiggins, David P. | Lewis, Gladius^;

Affiliations: Department of Mechanical Engineering, The University of Memphis, Memphis, TN 38152-3180, USA | Office of Admissions, The University of Memphis, Memphis, TN 38152-3180, USA

Note: [] Corresponding author. Tel.: +1 901 678 3266; Fax: +1 901 678 5459; E-mail: glewis@memphis.edu.

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.

Keywords: Weibull relationship, acrylic bone cement, fatigue

Journal: Bio-Medical Materials and Engineering, vol. 15, no. 5, pp. 349-355, 2005