title: Evaluation of flexural strength of hipped and presintered zirconia using different estimation methods of Weibull statistics.
abstract: OBJECTIVE
  This study determined the flexural strength of one hipped and eight presintered zirconia and evaluated the results using different estimation methods of Weibull statistics.
  
  
  METHODS
  Presintered zirconia specimens were prepared in white state and sintered according to each manufacturer's instructions. One hipped zirconia acted as the control group. The specimens were loaded in a Universal Testing Machine (ISO 6872, 2008). Data were analysed using "normal" (Levene test, one-way ANOVA, Scheffé test) and "Weibull distribution" estimated by either Least Squares (LS) (mean (Excel) and median rank (MINITAB)), Maximum Likelihood (ML) (MINITAB) or ML (MINITAB) with a correction of BS EN 843-5 (2006) (MLC) (alpha=0.05).
  
  
  RESULTS
  According to normal (σ) and Weibull distribution (s), three-point flexural strength (MPa) of the hipped zirconia (σ=1643 (1507; 1782), s(LS mean rank): 1772, s(LS median rank): 1751 (1619; 1894), s(ML): 1733 (1645; 1826) and s(MLC): (1625; 1848) showed significantly higher results compared to all other presintered zirconia groups (p<0.001). The lowest mean and characteristic strength was observed with GC (σ=817(803;953), s(LS mean rank): 935, s(LS median rank): 935(868; 1007), s(ML): 932(875; 994) and s(MLC): (862; 1009)). The highest Weibull modulus estimated by LS for mean and median rank was observed with LZ (8.9 and 9.8(7.5; 12.9), respectively) and the lowest with ZE (5.1 and 5(3; 8.2), respectively). According to ML and MLC estimation, the control group showed the highest (10.1(6.6; 15.6), 9.2(5.8; 14.2), respectively), and CZ the lowest (5.6(3.8; 8.2), 5.0(3.2; 7.8), respectively) Weibull modulus. No differences in estimates of standard deviations of the normal distribution and the estimates of Weibull moduli for different estimation methods were found between all tested groups.
  
  
  CONCLUSIONS
  Flexural strength of the tested hipped zirconia was higher than those of presintered ones according to both normal and Weibull distribution. LS (median rank) and ML estimates can be compared by a global test and by means of 95% CI. For corrected ML estimates the 95% CI can be interpreted. Estimate calculations in Excel (LS, mean rank) provides information on 95% CI for the Weibull parameters.
authors.affiliation: Clinic of Fixed and Removable Prosthodontics and Dental Material Science, Center of Dental Medicine, University of Zurich, 8032 Zurich, Switzerland. bogna.stawarczyk@zzm.uzh.ch
authors.forename: Bogna
authors.initials: B
authors.lastname: Stawarczyk
authors.forename: Mutlu
authors.initials: M
authors.lastname: Ozcan
authors.forename: Albert
authors.initials: A
authors.lastname: Trottmann
authors.forename: Christoph H F
authors.initials: CH
authors.lastname: Hämmerle
authors.forename: Malgorzata
authors.initials: M
authors.lastname: Roos
mesh_terms: D016018:Least-Squares Analysis; D016013:Likelihood Functions; D055595:Mechanical Phenomena; D016011:Normal Distribution; D018583:Pliability; D013223:Statistics as Topic; D015040:Zirconium / Q000737:chemistry*
chemical_list: D015040:Zirconium; C028541:zirconium oxide