This paper investigates the problem of robust fault detection for uncertain systems with missing measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurement missing phenomenon, which appears typically in a network environment, is modelled by a stochastic variable satisfying the Bernoulli random binary distribution. The focus is on the design of a robust fault detection filter, or a residual generation system, which is stochastically stable and satisfies a prescribed disturbance attenuation level. This problem is solved in the parameter-dependent framework, which is much less conservative than the quadratic approach. Both full-order and reduced-order designs are considered, and formulated via linear matrix inequality (LMI) based convex optimization problems, which can be efficiently solved via standard numerical software. A continuous-stirred tank reactor (CSTR) system is utilized to illustrate the design procedures.