Please cite this article in press as: Bütikofer L, et al. Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials. Dent Mater (2014), http://dx.doi.org/10.1016/j.dental.2014.11.014 ARTICLE IN PRESS DENTAL-2472; No. of Pages 18 d e n t a l m a t e r i a l s x x x ( 2 0 1 4 ) xxx.e1–xxx.e18 Available online at www.sciencedirect.com ScienceDirect jo ur nal home p ag e: www.intl.elsevierhealth.com/journals/dema Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials Lukas Bütikofer a , Bogna Stawarczyk b , Malgorzata Roos a,∗ a Division of Biostatistics, Institute of Social and Preventive Medicine, University of Zurich, Switzerland b Department of Prosthodontics, Dental School, Ludwig-Maximilians University, Munich, Germany a r t i c l e i n f o Article history: Received 31 October 2013 Received in revised form 9 April 2014 Accepted 3 November 2014 Available online xxx Keywords: Weibull modulus Weibull characteristic strength Least squares Failure probability Plotting positions Mean ranks Median ranks Hazen ranks Confidence interval Coverage a b s t r a c t Objectives. Comparison of estimation of the two-parameter Weibull distribution by two least squares (LS) methods with interchanged axes. Investigation of the influence of plotting positions and sample size. Derivation of 95% confidence intervals (95%CI) for Weibull param- eters applicable in the context of LS estimation. Preparation of a free available Excel template for computation of point estimates and 95%CI for Weibull modulus (m) and characteristic strength (s). Methods. Monte Carlo simulation covering a wide range of Weibull parameters and sample sizes. Mathematical derivation of formulae for computation of 95%CI according to a Menon- type approach for both m and s. Empirical proof that the practically observed coverage agrees with the nominal one of 95%. Results. Relative and absolute performance of LS estimators depended on sample size, plotting positions and parameter to be estimated. For most situations they outperformed the corresponding Maximum Likelihood (ML) estimator in terms of bias, while precision was almost the same. Naïve Wald-type 95%CI based on standard errors of LS regression coefficients did not reach targeted coverage. An easy-to-apply alternative based on asymp- totic standard errors (Menon 95%CI) resulted in excellent coverage. Conclusion. Accuracy of the LS methods for Weibull modulus and characteristic strength essentially depend on plotting position and sample size. Large sample sizes (n ≥ 30) support a credible Weibull parameters estimation. An important complement of the point estimates of Weibull parameters is provided by the Menon 95%CI. A free available Excel template considerably facilitating computation of point and interval estimates of Weibull parameters is provided. © 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. 1. Introduction Dental restorative ceramics have excellent properties in terms of esthetics [1] and biocompatibility [2] but are susceptible to ∗ Corresponding author at: Hirschengraben 84, 8001 Zurich, Switzerland. Tel.: +41 44 634 46 48. E-mail address: mroos@ifspm.uzh.ch (M. Roos). brittle fracture, a type of failure that is particularly difficult to predict. In general, ceramics are sensitive to defects or flaws within the material, motivating the application of probabilis- tic concepts and in particular the weakest link (or largest flaw) model. When measuring the flexural strength of a material, http://dx.doi.org/10.1016/j.dental.2014.11.014 0109-5641/© 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.