Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution

Abstract

It is generally assumed that the measured strength of brittle ceramics follows a Weibull distribution. However, there seems to be few sound and direct evidences to support this assumption. Several previous studies have shown that other distributions, such as normal distribution and log-normal distribution may describe more appropriately the strength data than Weibull distribution. In this paper, the efficiency of using a normal distribution to describe the strength which follows a Weibull distribution is examined based on Monte-Carlo simulations. It was shown that there exist strong correlations between the parameters of normal distribution and those of Weibull distribution. For the designed fracture probability not lower than 0.01, analyses based on both normal distribution and Weibull distribution may give nearly identical predictions for the applicable stress levels. For lower fracture probabilities, the differences between the predictions of both distributions are not significant. It was suggested that, if there is no evidence to confirm that the measured strength follows a certain distribution, normal distribution and Weibull distribution seem to have the same efficiency in analysing the statistical variations in the measured strength of ceramics.

Reliability analysis of subway sliding plug doors based on improved FMECA and Weibull distribution

“…Since its development, it has been widely used in the fields of probability distribution description [13], lifetime prediction [39], reliability assessment [25], and maintenance program development [15]. Meanwhile, literature [23] points out that the service life of the subway sliding plug door system obeys the Weibull distribution, so this paper chooses the Weibull distribution to predict the door's remaining life and the Weibull distribution function is shown as follows:…”

“…Door leaf FM 12 The glass is broken 2 FM 13 Deformation and peeling of sealing tape 4 FM 14 Fractured hinges 4 Cutting out the travel switch S2 FM 15 Functional fault 6 Screw FM 16 Poor lubrication 3 Isolation locking device FM 17 Functional fault…”

Investigation of Variability of Flaw Strength Distributions on a Brittle SiC Ceramic

“…The parameters of the Weibull cumulative distribution functions (CDF) were estimated using the Maximum Likelihood Estimation Method and the Moment Method [18,26,27].…”