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We consider a supply chain that faces a potential brand crisis, with one manufacturer deciding quality improvement and global advertising levels, and one retailer determining local advertising effort. The goodwill model is adopted here under the assumption that when the crisis happens, the companies suffer a sharp decrease in the goodwill. We characterize the feedback Nash equilibrium, and then we compare the corresponding quality and advertising strategies and outcomes with those of the case where the potential crises are absent, and where the companies do not invest in quality. The effects of the instantaneous crisis rate and the short-term and long-term damages are also evaluated. Our results reveal that the pre-crisis quality improvement accelerates the goodwill build-up before the crisis, and also helps the recovery in post-crisis regime. Its twofold function suggests that one of the pre- and post-crisis regimes/instants ought to be matched with more intense investment in both quality and global advertising, depending on the overall effect of instantaneous crisis rate, short-term damage and long-term damage. This carryover effect also brings a non-monotonicity of quality improvement effort and value functions with respect to the instantaneous crisis rate. These properties leave the chance to mitigate the loss by anticipating crisis for both members under certain circumstances.