To increase the precision and reliability of process control, random uncertainty factors affecting the control system must be accounted for. We propose a novel approach based on the operational matrix technique for robust PI controller design for dead-time processes with stochastic uncertainties in both process parameters and inputs. The use of the operational matrix drastically reduces computational time in controller design and statistical analysis with a desired accuracy over that of the traditional Monte-Carlo method. Examples with deterministic and stochastic inputs were considered to demonstrate the validity of the proposed method. The computational effectiveness of the proposed method was shown by comparison with the Monte-Carlo method. The proposed approach was mainly derived based on the integrator plus dead-time process, but can be easily extended to other types of more complex stochastic systems with dead-time, such as a first-order plus dead-time or a second-order plus dead-time system.