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Increased customer expectations have resulted in new product developments at an ever increasing pace.Moreover engineered systems become far more complex and compact.Under this circumstance, it is challenging to develop an engineering product with high product reliability and process quality.This research is particularly concerned about assembly quality prediction where the assembly quality is governed by assembly tolerances defined as a function of field variables (x, y, z) in parts.The field variables generally contain manufacturing variability to some degree.Examples include assembly gap tolerance of multiple bodies where the gap tolerance is defined in terms of field variables.This research thus develops an assembly gap prediction model using a 3D random field characterization technique.The gap prediction modeling employs four-step procedures: (a) 3D scanning for assembly parts, (b) random field characterization of scanning data, (c) development of an assembly quality prediction model, and (d) model validation.First, 3D scanning should be performed for key parts in the assembly, which could affect the assembly quality significantly.Second, the scanned field data is statistically characterized using the proper orthogonal decomposition (POD) while taking into account statistical dependency among the field data.Third, a data-driven approach is used to develop the assembly quality prediction model based on the assembly model and random field data in parts.This prediction model is useful for screening defective parts before the assembly.Finally the model is validated with some test samples.For the demonstration purpose, the proposed method is applied to predict the battery cover assembly gap in a smartphone.The results show that the assembly gap prediction model is suitable for predicting the defective battery cover before it is assembled to the smartphone.