Cardiac repolarization alternans is an electrophysiologic condition identified by a beat-to-beat fluctuation in action potential waveform. It has been mechanistically linked to instances of T-wave alternans, a clinically defined ECG alternation in T-wave morphology, and associated with the onset of cardiac reentry and sudden cardiac death. Many alternans detection algorithms have been proposed in the past, but the majority have been designed specifically for use with T-wave alternans. Action potential duration (APD) signals obtained from experiments (especially those derived from optical mapping) possess unique characteristics, which requires the development and use of a more appropriate alternans detection method. In this paper, we present a new class of algorithms, based on the Monte Carlo method, for the detection and quantitative measurement of alternans. Specifically, we derive a set of algorithms (one an analytical and more efficient version of the other) and compare its performance with the standard spectral method and the generalized likelihood ratio test algorithm using synthetic APD sequences and optical mapping data obtained from an alternans control experiment. We demonstrate the benefits of the new algorithm in the presence of Gaussian and Laplacian noise and frame-shift errors. The proposed algorithms are well suited for experimental applications, and furthermore, have low complexity and are implementable using fixed-point arithmetic, enabling potential use with implantable cardiac devices.