We simulated the variability in measured quartz optically stimulated luminescence (OSL) signals and dose response curves (DRCs) caused by measurement uncertainties, including counting statistics and instrumental irreproducibility. We find that these measurement errors can give rise to large variations in the observed luminescence signal and contribute to among-aliquot or among-grain scatter in DRCs and equivalent dose (De) values. Different measurement systems (i.e., luminescence readers) may have different counting statistics properties and, hence, may exhibit differing extents of variation in the observed OSL signal, even for the same sample. Our simulation shows that the random measurement uncertainties may result in some grains or aliquots being ¿saturated¿ (that is, the measured natural signal is consistent with, or lies above, the saturation level of the measured DRC) and that the rejection of these ¿saturated¿ grains may result in a truncated De distribution, with De underestimation for samples with natural doses close to saturation (e.g., twice the characteristic saturation dose, D0). We propose a new method to deal with this underestimation problem, in which standardised growth curves (SGCs) are established and the weighted-mean natural signal (Ln/Tn) from all measured grains is projected on to the corresponding SGCs to determine De. Our simulation results show that this method can produce reliable De estimates up to 5D0, which is far beyond the conventional limit of ¿2D0 using the standard SAR procedure.