Fracture toughness of materials. Titanium diboride is an extremely hard ceramic material known for its resistance to mechanical erosion or fracture. The fracture toughness of the material, measured in mega Pascals per meters squared (MPa/m²), was modeled using the Weibull distribution in Quality Engineering (Vol. 25, 2013). One possible set of Weibull parameters for this data is α = 6 and β = 1800.
a. Find the mean and variance of the fracture toughness for this material.
b. Provide an estimate of the proportion of fracture toughness values that lie within 2 standard deviations of the mean.
c. Use the Weibull cumulative distribution function to calculate the exact probability that fracture toughness falls within 2 standard deviations of the mean. Compare the result with your answer in part b.