ISO 20501 pdf download – Fine ceramics (advanced ceramics,advanced technical ceramics)-Weibull statistics for strength data

ISO 20501 pdf download – Fine ceramics (advanced ceramics,advanced technical ceramics)-Weibull statistics for strength data.
5.2 This document provides two approaches, method A and method B. which are appropriate for different purposes.
Method A provides a simple analysis for circumstances in which the nature of strength-defining flaws
Is either known or assumed to be from a single population. Fractography to identify and group test
Items with given flaw types Is thus not required, This method Is suitable for use for simple material
screening.
Method B provides an analysis for the general case in which competing flaw populations exist. This method is appropriate for final component design and analysis. The method requires that fractography be undertaken to identify the nature of strength-limiting flaws and assign failure data to given flaw population types.
5.3 In method A. a strength data set can be analysed and values of the Weihull modulus and characteristic strength (rn,oo) are produced, together with confidence bounds on these parameters. If necessary the estimate of the mean strength can be computed. Finally, a graphical representation of the failure data along with a test report can be prepared. It should he noted that the confidence bounds are Frequently widely spaced, which indicates that the results of the analysis should not be used to extrapolate far beyond the existing bounds of probability of failure. A necessary assumption for a valid extrapolation (with respect to the tested effective volume Vg and/or small probabilities of failure) Is that the flaw populations in all considered strength test pieces are of the same type.
5.4 In method B, begin by performing a fractographic examination of each failed specimen in order to characterize fracture origins. Screen the data associated with each flaw distribution for outliers. If all failures originate from a single flaw distribution compute an unbiased estimate of the Weibull modulus. and compute confidence bounds for both the estimated Weibull modulus and the estimated Weibull characteristic strength. If the failures originate from more than one flaw type, separate the data sets associated with each flaw type, and sublect these individually to the censored analysis. Finally, prepare a graphical representation of the failure data along with a test report. When using the results of the analysis for design purposes it should be noted that there is an implicit assumption that the flaw populations In the strength test pieces and the components arc of the same types.
6 Method A: maximum likelihood parameter estimators for single flaw populations
6.1 General
This document outlines the application of parameter estimation methods based on the maximum likelihood technique (see also References 1131, 114J. IZQJ and IZI]). This technique has certain advantages. The parameter estimates obtained using the maximum likelihood technique are unique (for a two-parameter Weibufl distribution), and as the size of the sample increases, the estimates statistically approach the true values of the population more efficiently than other parameter estimation techniques.
6.2 Censored data
The application of the techniques presented in this document can be complicated by the presence of test specimens that tail from extraneous flaws, fractures that originate outside the effective gauge section. and unidentified fracture origins. If these complications arise, the strength data from these specimens should generally not be discarded. Strength data from specimens with fracture origins outside the effective gauge sectionLJl and from specimens with fractures that originate from extraneous flaws should be censored, and the maximum likelihood methods presented in method B (CLausel) arc applicable. It is Imperative that the number of unidentified fracture origins, and how they were classified, be stated in the test report. A discussion of the appropriateness of each option can be found inZZ2.
Applying the censored analysis implies that it is assumed that the flaw populations are concurrent. This isa choice, which should be Indicated In the test report.
6.3 Likelihood Functions
The likelihood function for the two parameter Welbull distribution of a sample with a single flaw populationLI is defined by Formula (14).