Their review focuses on where to locate the sensors in every physical area to increase the sensing coverage [12; 13], lifetime, and energy savings [14; 15] at minimum costs [16]. Other sensor-deployment research focuses on the location of an estimated product feature or parameter that a sensor measures instead of the place where the sensor is physically installed. Therefore, the number and location of sensors must be based on the product features or parameters to be measured [6]. From this perspective, the challenge of designing a sensor system is selecting product features or parameters to measure in different industrial application scenarios [17]. [PERSON] et al. [18] suggested a sensor distribution for variation diagnosis in a multistation assembly process. Using a state-space model, a diagnosability index was developed to quantify the effectiveness of the sensor distribution. The variational transmissibility between stations was considered, and a backward propagation strategy was designed to determine the measurement stations. [PERSON] et al. [19] created an optimal sensor allocation for root-cause analysis that maximizes the number of measurement points placed at key characteristics (KCs). The critical product and process design features are considered, and a feature-based procedure is presented to include arbitrary locations and KCs in the final sensor layout. [PERSON] et al. [20] proposed a quantitative cause-effect graph (QCEG) to handle the heterogeneity among the properties of sensors and faults. The QCEG models the cause-effect relationship between the system faults and sensor readings. Based on minimizing the fault unobservability, sensor deployment is performed to facilitate single-station multistep manufacturing process monitoring. [PERSON] et al. [21] investigated the effects of sensor allocation optimization on the diagnosability of a multistation manufacturing system (MMS). They proposed three indices (detectability, locatability, and isolatability) to measure the system's diagnosability. A two-step process is presented to specify the variable transmission between stations and variation diagnosis within a station. Based on an established definition of sensor allocation in a Bayesian network (BN), [PERSON] et al. [22] developed a \"best allocation subsets by intelligent search\" (BASIS) algorithm to identify the optimal sensor allocation at minimum cost under different specified average run length (ARL) requirements. They designed a diagnosis ranking method to determine the root cause by ranking all the identified potential faults in a manufacturing system. Considering the effects of the propagation of fault risks, [PERSON] et al. [23] proposed a gray relational analysis (GRA)-based quantitative causal diagram (QCD) sensor allocation strategy to describe the fault-sensor and fault-to-fault causal relationships. The data-driven-based GRA calculates the coefficients of the fault risk propagation. [PERSON] et al. [24] proposed an information theory-based optimal sensor placement (OSP) framework for parameter estimation and strain estimation considering sensor costs. A Bayesian OSP method combined with modal expansion is used to minimize the information entropy regarding the strain time histories at critical locations of an offshore wind turbine. A multi-objective function is proposed to balance sensor costs and information entropy balanced by the weight factor. It was found that the OSP results are sensitive to the weight factor; the Pareto solutions for OSP are also presented. From this literature review, it is clear that previous studies in this area do not address certain key concerns:  
1. Although many papers describe the causal model between faults and sensors for variation diagnosis in complex manufacturing systems based on the sensor distribution, they lack a causal analysis of the key physical parameters closely related to fault characteristics and their critical quantitative representation. 2.