Components such as bladed rings, and bladed disks fabir-icated out of titanium matrix composites were extensively explored in the two decades since about 1990 as light weight replacements for conventional superalloy blades and disks in the intermediate hot stages of gas turbines. One of the challenges, which has hindered their adoption is the relative unreliability of the composite components; nominally identical Ti composite specimen display a much larger variability in strength than their superalloy counterparts. In the present work, we have quantified the reliability of Ti matrix composites by developing a detailed micromechanical-statistical model of their failure. The micromechanical model resolves fibres, matrix, and the interface, and accounts for such failure modes as fibre breakage, matrix cracking, matrix plasticity, interfacial sliding, and debonding. It also accounts for mechanical interaction between these various failure modes. The mechanical model’s predictions are validated against synchotron X-ray measurements reported in the literature, both after loading, and unloading. Using the detailed micromechanical model, Ti matrix composite was simulated following a Monte Carlo framework. These simulations yield the empirical strength distribution of the Ti matrix composite, and insights into the dominant failure mode. The latter allows the construction of a stochastic model of composite failure. The stochastic model can be used to determine safe working loads as a function of composite size for any desired reliability level. Copyright © 2017 ASME.