Some problems in application of three-parameter Weibull distributions to reliability evaluation of ceramics

Abstract

When applying ceramics to machine components, the probabilistic approach or reliability engineering approach is useful to handle rather large scatter in the strength of ceramics. This has led to the development of reliability evaluation systems in several countries. Up to the present time, the two-parameter Weibull distribution has most often been used for ceramics. However, use of the three-parameter one will also be important in the near future. Thus, this review addresses application of the three-parameter Weibull distribution in relation to reliability evaluation of ceramic components, and some problems to be encountered in its application are discussed. The problems discussed include methods for parameter estimation, the relationship between the shape parameter and degree of scatter, the definition of the effective volume, extension of the three-parameter Weibull distribution to polyaxial stress-states and the stress-state dependence of the shape parameter. In particular, the last two problems are examined in detail. Probabilistic design methodology using the three-parameter Weibull distribution is also discussed.