Diametral compression strength distributions and the compaction behavior and of irregular shape 150--200 {mu}m ceramic granules and uniform-size 210 {mu}m glass spheres were measured to determine how granule strength variability relates to compaction behavior of granular assemblies. High variability in strength, represented by low Weibull modulus values (m<3) was observed for ceramic granules having a distribution of sizes and shapes, and for uniform-size glass spheres. Compaction pressure data were also analyzed using a Weibull distribution function, and the results were very similar to those obtained from the diametral compression strength tests for the same material. This similarity suggests that it may be possible to model granule compaction using a weakest link theory, whereby an assemblage of granules is viewed as the links of a chain, and failure of the weakest granule (i.e., the weakest link) leads to rearrangement and compaction. Additionally, with the use of Weibull statistics, it appears to be possible to infer the variability in strength of individual granules from a simple pressure compaction test, circumventing the tedious task of testing individual granules