In-vessel tungsten components of a future demonstration fusion reactor are likely to be operated in the material's non-ductile regime. Assessment of the components' reliability is not possible with current ductile design codes or through experimental qualification. There is therefore an urgent need for non-ductile assessment procedures. One such approach currently considered is Weibull's weakest link theory, which is based on linear-elastic fracture mechanics and has its origins in ceramics. A full assessment of its validity has been performed, and the challenge of obtaining irradiated material data addressed.Bend tests at the macroscopic scale confirm previous findings that the scatter in strength of pure tungsten follows a two-parameter Weibull distribution, provided the material fractures within its elastic regime. However, tests conducted over a range of specimen sizes reveal the technique's shortcomings in accurately predicting the material's size effect in fracture, questioning its applicability to pure tungsten and also other brittle metallic materials.Fracture strength tests conducted at the micrometre scale through cantilever bending have addressed the challenge of obtaining irradiated material data. An ultra-fine grained self-passivating tungsten alloy, considered as an alternative contender to tungsten for in-vessel components, is shown to fracture within its linear-elastic regime at the microscopic scale. A reliable and repeatable measurement of its strength of approximately 5.9 GPa is obtained. The scatter in measurements is shown to be greater than random errors, and to be described well by a two-parameter Weibull distribution. Cantilever tests conducted over a range of specimen sizes reveal a strong size effect (4.3 - 9.0 GPa), which is accurately predicted by Weibull's weakest link theory.Ion implantations, conducted in the tungsten alloy to mimic neutron induced elastic collision damage, result in a statistically confirmed drop (6 %) in cantilever measured fracture strength at low doses (0.7 dpa), and an increase (9-16 %) at higher doses (7 dpa).The cantilever test technique is therefore suitable for the measurement of ion and neutron irradiation effects on the material's fracture strength. Provided a full validation of Weibull's weakest link theory strength extrapolation from the micro- to macroscopic scale is realised on a future heterogeneity free material batch, irradiated material data obtained from cantilever tests could be used to assess the reliability of in-vessel components fabricated from a self-passivating tungsten alloy, and fill the current gap in non-ductile design assessment procedures.