This paper proposes a system reliability model of coordinate sensor systems used for manufacturing process fault diagnosis. The system working condition is derived based on engineering knowledge and the least squares fault diagnosis algorithm when considering the sensor failure mode of sensor precision degradation. It turns out that the system working conditions are the same as those of the so-called series-weighted- k-out-of-n systems. When applying the existing algorithms for series-weighted-k-out-of-n systems in real manufacturing situation, however, an exponential computational time is needed as the coefficients are not in a discrete scale. In order to overcome this difficulty, a weight interval method is developed in this paper to evaluate the upper bound and lower bound of system reliability efficiently. A case study for an automotive body assembly process is used to demonstrate the developed model and algorithms.