In this letter we generalize Spekkens notion of measurement non-contextuality (NC). We show that any non-contextual ontological model based on this notion of contextuality fails to explain the statistics of outcomes of a single carefully constructed POVM executed sequentially on a quantum system. The POVM essentially forms a single measurement device. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual ontic model, and construct corresponding quantum situations where the measurement outcomes from the device violate this NC inequality. Our work brings out the hitherto unexplored implications of contextuality for a single measurement device, and paves the way for further study of consequences of contextuality for sequential measurements.
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