The recent development of feature extraction algorithms with multiple layers in machine learning and pattern recognition has inspired many applications in multivariate statistical process monitoring. In this work, two existing multilayer linear approaches in fault detection are reviewed and a new one with extra layer is proposed in analogy. To provide a general framework for fault diagnosis in succession, this work also proposes the contribution propagation analysis which extends the original definition of contribution of variables in multivariate statistical process monitoring. In fault diagnosis stage, the proposed contribution propagation analysis for multilayer linear feature extraction algorithms is compared with the fault diagnosis results of original contribution plots associated with single layer feature extraction approach. Plots of variable contributions obtained by the aforementioned approaches on the data sets collected from a simulated benchmark case study (Tennessee Eastman process) as well as an industrial scale multiphase flow facility are presented as a demonstration of the usage and performance of the contribution propagation analysis on multilayer linear algorithms.