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Optimal sensor allocation can substantially reduce the life cycle maintenance costs of engineering systems. Considerable effort has been exerted to model the causal relationship between sensors and faults, but without considering the propagation of fault risk. In this paper, a grey relational analysis (GRA) based quantitative causal diagram (QCD) sensor allocation strategy is proposed that can take account of the influence of the propagation of fault risk. QCD is used to describe both the fault-sensor causal relationship and the fault-to-fault causal relationship. A data-driven-based GRA is applied in QCD to calculate the coefficients of the propagation of fault risk. To achieve an accurate relationship between faults and sensors, an improved quantitative analytic hierarchy process is proposed to calculate the coefficients between faults and sensors that is defined as sensor detectability in this paper. An optimal sensor allocation strategy is then developed using an improved particle swarm optimization (IPSO) algorithm under the constraint on sensor detectability to minimize fault unobservability and total cost. The proposed strategy is demonstrated by a case study on a single-phase inverter system. Compared with two other sensor allocation strategies, the results show that the proposed strategy can obtain the lowest fault unobservability of per unit cost (−0.242) for sensor allocation under the propagation of fault risk. [ABSTRACT FROM AUTHOR]