Ceramics have low toughness as determined by testing under a tensile load; often, ceramics have 
  
    
      
        
          
            K
          
          
            
              c
            
          
        
      
    
    {\textstyle \mathrm {K} _{\mathrm {c} }}
   values that are ~5% of that found in metals. However, ceramics are usually loaded in compression in everyday use, so the compressive strength is often referred to as the strength; this strength can often exceed that of most metals. However, ceramics are brittle and thus most work done revolves around preventing brittle fracture. Due to how ceramics are manufactured and processed, there are often preexisting defects in the material introduce a high degree of variability in the Mode I brittle fracture. Thus, there is a probabilistic nature to be accounted for in the design of ceramics.
The Weibull distribution predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture. Fiber bundles
To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce  in 1926 as a model to understand the strength of composite materials. The bundle consists of a  large number of parallel Hookean springs of identical length and each having identical spring constants. They have however different breaking stresses. All these springs are suspended from a rigid horizontal platform. The load is attached  to a horizontal platform, connected to the lower ends of the springs. When this lower platform is absolutely rigid, the load at any point of time is shared equally (irrespective of how many fibers or springs have broken and where) by all the surviving fibers. This mode of load-sharing is called Equal-Load-Sharing mode. The lower platform can also be assumed to have finite rigidity, so that local deformation of the platform occurs wherever springs fail and the surviving neighbor fibers have to share a larger fraction of that transferred from the failed fiber. The extreme case is that of local load-sharing model, where load of the failed spring or fiber is shared (usually equally) by the surviving nearest neighbor fibers. Disasters
Failures caused by brittle fracture have not been limited to any particular category of engineered structure.