A practical and systematic review of Weibull statistics for reporting strengths of dental materials

Abstract

Objectives To review the history, theory and current applications of Weibull analyses sufficient to make informed decisions regarding practical use of the analysis in dental material strength testing. Data References are made to examples in the engineering and dental literature, but this paper also includes illustrative analyses of Weibull plots, fractographic interpretations, and Weibull distribution parameters obtained for a dense alumina, two feldspathic porcelains, and a zirconia. Sources Informational sources include Weibull's original articles, later articles specific to applications and theoretical foundations of Weibull analysis, texts on statistics and fracture mechanics and the international standards literature. Study Selection The chosen Weibull analyses are used to illustrate technique, the importance of flaw size distributions, physical meaning of Weibull parameters and concepts of “equivalent volumes” to compare measured strengths obtained from different test configurations. Conclusions Weibull analysis has a strong theoretical basis and can be of particular value in dental applications, primarily because of test specimen size limitations and the use of different test configurations. Also endemic to dental materials, however, is increased difficulty in satisfying application requirements, such as confirming fracture origin type and diligence in obtaining quality strength data.

Marginal adaptation, fracture load and macroscopic failure mode of adhesively luted PMMA-based CAD/CAM inlays

“…Weibull statistics are considered appropriate to characterise the structural reliability of brittle dental materials [44][45][46]. A higher Weibull modulus indicates lower variability of strength, due to flaws and defects in the material [47,48].…”

Evaluation of bond strength of resin cements using different general-purpose statistical software packages for two-parameter Weibull statistics

“…In such a case the following probability density function is obtained. Frequently the Weibull statistic is computed based on the statistical approach [14,15].…”

“…which holds under the assumption of the independence of the realisations x i from the Weibull distribution with parameters s and m [15,26,27,32]. ML estimation has attractive mathematical properties for large samples such as consistency, asymptotic normality and asymptotic efficiency [21].…”

“…In addition, when using ML it is not necessary to use any formula for determination of the plotting positions . Quinn and Quinn [15] mention that the ML estimate for the characteristic strength has negligible bias, but small correction factor is usually applied to correct or "unbias" the Weibull modulus estimate…”

“…Data of mechanical tests of materials may be analysed by a Weibull distribution in which failure probability can be predicted at any level of stress, providing information about the variability of the results and reflecting the structural precision of the materials or bonded assemblies [15][16][17][18][19][20]. Three-or two-parameter Weibull distributions can be considered.…”