Pyrolysis is the thermochemical process that leads to the ignition of a solid fuel and a key mechanism in flame spread and fire growth. Because polymeric materials are flammable and ubiquitous in the modern environment, the understanding of polymer pyrolysis is thus essential to tackle accidental fires. In this paper, we used transient irradiation as an external source of heat to study the process of pyrolysis and ignition of a polymer. While previous ignition studies use constant irradiation, transient irradiation is the most frequent condition found in accidental fires, but it lacks a theoretical framework since it has been ignored in the literature. Moreover, transient irradiation is a more comprehensive case for the understanding of pyrolysis where nonlinear heat transfer effects challenge the validity of solid-phase criteria for piloted ignition developed previously. We propose here that transient irradiation is the general problem to solid fuel ignition of which constant irradiation is a particular case. In order to investigate how this novel heat source influences polymer pyrolysis and flammability, numerical simulations and experiments have been conducted on poly(methyl methacrylate) (PMMA) samples 100 mm by 100 mm and 30 mm deep exposed to a range of parabolic pulses of irradiation. The 1D model, coded in GPyro, uses heat and mass transfer and single-step heterogeneous chemistry, with temperature dependent properties. The predictions are compared to experiments conducted in the cone calorimeter for the constant irradiation and the Fire Propagation Apparatus for transient irradiation. The experiments validate the temperature predictions of the model and also provide the time to ignition. The model then complements the experiments by calculating the mass loss rate. A series of 16 parabolic pulses (including repeats) are investigated with a range of peak irradiation from 25 to 45 kW/m(2), while the time to peak ranges from 280 to 480 s. For these pulses, the time to ignition measurements range from 300 to 483 s. The model can predict the in-depth temperature profiles with an average error lower than 9%. Model and experiments are then combined to study the validity of the solid-phase criteria for flaming ignition found in the literature, namely critical temperature, critical mass loss rate, critical energy and critical time-energy squared. We find that of these criteria, the best predictions are provided by the critical mass loss rate followed by the critical temperature, and the worst is the critical energy. Further analysis reveals the novel concept of simultaneous threshold values. While the mass loss rate is below 3 g/m(2) and the surface temperature is below 305 degrees C, ignition does not occur. Therefore these threshold values when exceeded simultaneously establish the earliest time possible for ignition. (C) 2015 The Authors. Published by Elsevier Inc. on behalf of The Combustion Institute.