Online　estimation　for　product　quality　is　crucial　for　improving　industrial　process　efficiency.　However,　model　degradation　and　outliers　usually　challenge　industrial　quality　estimation　models.　To　tackle　the　above　problems,　a　robust　self-constructing　fuzzy　neural　network　(RSC-FNN)　is　developed　in　the　article.　In　the　RSC-FNN,　the　rules　can　be　automatically　created　or　pruned,　obtaining　the　online　self-constructing　mechanism　(OSCM).　First,　an　online　error　compensation　algorithm　is　developed　to　generate　new　rules.　Second,　the　model　performance　and　contribution　of　existing　rules　are　evaluated　online　to　delete　redundant　rules.　Thus,　the　OSCM　effectively　improves　the　structural　adaptability　and　compactness　of　the　RSC-FNN.　Moreover,　the　correntropy-induced　criterion,　which　can　handle　complex　outliers,　is　modified　for　the　parameter　learning　algorithm.　Hence,　the　adverse　effect　of　outliers　can　be　suppressed　during　the　parameter　updating　process.　Besides,　we　analyze　the　convergence　of　the　RSC-FNN　to　ensure　its　feasibility　in　industrial　applications.　Finally,　two　industrial　applications　are　studied　to　test　the　effectiveness　of　the　RSC-FNN.　Compared　with　other　FNNs,　the　results　indicate　that　the　RSC-FNN　performs　better　in　learning　efficiency,　structure　compactness,　and　robustness.　IEEE