title: 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 (V(0)), 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 V(0) obtained is less than or greater than zero, respectively.
authors.affiliation: Department of Mechanical Engineering, The University of Memphis, TN 38152-3180, USA.
authors.forename: Sied
authors.initials: S
authors.lastname: Janna
authors.forename: David P
authors.initials: DP
authors.lastname: Dwiggins
authors.forename: Gladius
authors.initials: G
authors.lastname: Lewis
mesh_terms: D000465:Algorithms; D002484:Cementation / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008422:Materials Testing / Q000379:methods*; D008956:Models, Chemical; D015233:Models, Statistical; D019904:Polymethyl Methacrylate / Q000032:analysis* / Q000737:chemistry*; D012044:Regression Analysis; D016008:Statistical Distributions; D013718:Tensile Strength
chemical_list: D019904:Polymethyl Methacrylate