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To meet OBD norms for exhaust gas oxygen sensor component, there are various methods developed to monitor health of the same in engine management system. Here a new diagnosis strategy for exhaust gas oxygen sensor response is proposed, mainly applicable for start-stop vehicles. This diagnosis strategy is executed during the change in engine running state to stop state due to start-stop feature. In general, before the engine stop is triggered, the lambda in the engine can be rich or lean; then when engine is stopped, fuel injection is cut-off and only air passes through. Due to inertia of engine rotation after fuel cut-off, this air is still passed across oxygen sensor in exhaust path. So here if lambda before fuel cut-off is maintained rich, then rich to lean (i.e. air) transition is realized by oxygen sensor. These are transitions where the oxygen sensor response is evaluated having the coordination with start-stop module.