In multi-stage manufacturing systems, optimisation of part quality inspection planning (PQIP) problem means to determine the optimal time, place and extent of inspection activities for assessing the significant quality characteristics of products while maximising the system efficiency. An inspection activity is capable of detecting the produced defects partially and accordingly prevents further processing of them in downstream and more importantly avoids them to reach customers. In this paper, the existing researches on the optimisation of the part quality inspection are surveyed from the viewpoint of the considered production system characteristics; the applied modelling approaches and solution methodologies. This review found that although numerous works have been already done on the PQIP, the development of multi-objective optimisation frameworks considering real production constraints under parameters uncertainty is necessary. Also, by the Industry 4.0 trend, the creation of integrated models aiming to plan the inspection, maintenance and production activities simultaneously, seems to be an important potential future research direction.