This work presents a practical scheme to attain PI achievable performance (the performance achievable with a proportional integral (PI) controller) for linear SISO processes with dead time driven by stochastic disturbances. It uses a combination of a quantitative measure called Control Loop Performance Index (CLPI) and signature plots of the closed loop disturbance impulse response (IR) to arrive at PI achievable performance in an iterative manner. The proposed methodology requires only routine operating data and knowledge of the process delay, and its efficacy is illustrated through several case studies.