Nuclear burning and its dependence on the mass accretion rate are fundamental ingredients for describing the complicated observational phenomenology of neutron stars in binary systems. Motivated by high quality burst rate data emerging from large statistical studies, we report general calculations relating bursting rate to mass accretion rate and neutron star rotation frequency. In this first work we neglect general relativistic effects and accretion topology, though we discuss where their inclusion should play a role. The relations we derive are suitable for different burning regimes and provide a direct link between parameters predicted by theory and what is to be expected in observations. We illustrate this for analytical relations of different unstable burning regimes that operate on the surface of an accreting neutron star. We also use the observed behaviour of burst rate to suggest new constraints on burning parameters. We are able to provide an explanation for the long standing problem of the observed decrease of burst rate with increasing mass accretion that follows naturally from these calculations: when accretion rate crosses a certain threshold, ignition moves away from its initially preferential site and this can cause a net reduction of the burst rate due to the effects of local conditions that set local differences in both burst rate and stabilization criteria. We show under which conditions this can happen even if locally the burst rate keeps increasing with accretion.
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