This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed within the latent variable modeling framework and can be used to evaluate the degree to which coefficient alpha underestimates scale reliability in empirical measurement research employing such instruments. The approach is straight-forwardly utilized with readily available software and is illustrated using a numerical example.