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Goal recognition design involves the offline analysis of goal recognition models by formulating measures that assess the ability to perform goal recognition within a model and finding efficient ways to compute and optimize them. In this work we relax the full observability assumption of earlier work by offering a new generalized model for goal recognition design with non-observable actions. A model with partial observability is relevant to goal recognition applications such as assisted cognition and security, which suffer from reduced observability due to sensor malfunction or lack of sufficient budget. In particular we define a worst case distinctiveness (wcd) measure that represents the maximal number of steps an agent can take in a system before the observed portion of his trajectory reveals his objective. We present a method for calculating wcd based on a novel compilation to classical planning and propose a method to improve the design using sensor placement. Our empirical evaluation shows that the proposed solutions effectively compute and improve wcd.