Use or Abuse of Weibull Statistics in Dental Materials Science

Objectives: Weibull statistical methods are increasingly used in the analysis of strength data of dental biomaterials. However, there is controversy regarding appropriate sample sizes, data exploration and distribution fitting and in the fundamental assumptions made when Weibull methods are used to analyze data generated from the mechanical testing of polymers and composites. The aim is to explore the validity of using a Weibull statistical approach in the analysis of strength data of dental ceramics and resin-based composites with a particular focus on strength-scaling.

Methods: A microhybrid (Filtek Z100), a nanofilled (Filtek Supreme) and a flowable (Filtek Supreme Flow) resin-based composite; a feldspathic porcelain (Vita VM7) and a soda lime glass were investigated. 180 nominally identical disc-shaped specimens (12 mm diameter and 1 mm thickness) were fabricated for each material and divided into two groups (n=90). Bi-axial flexure strength (BFS) was determined using a ball-on-ring (BoR) and a ring-on-ring (RoR) configuration for each material to generate different effective volumes under tensile stressing and allow exploration of size-strength effects. The Weibull parameters and associated 95% confidence intervals were calculated for increasing sample sizes to n=90. Size-strength relationships were explored for each material and compared with theoretical values.

Results: All materials except the flowable composite demonstrated significantly increased BFS when tested in a BoR as opposed to a RoR configuration (P<0.05). The Weibull moduli of the microhybrid, nanofilled and soda lime specimens were not significantly altered when loaded with different effective volumes under stress as the 95% confidence intervals overlapped. The theoretical RoR BFS value predicted from experimental determination of BoR BFS correlated well for all resin composites apart from the flowable material.

Conclusions: The observed variability in the size-strength relationships suggests that caution should be taken to avoid unjustified use of Weibull analyses as extrapolation of findings potentially could become erroneous.