Cronbach's alpha has been used as a golden standard reliability criterion. Although psychometricians have long been pointed out that the alpha is not the most appropriate way to examine reliability, the gap between psychometrics and psychology has impeded the application of other reliability measures. However, recently the interest has been growing many papers have published recommendations for alternative reliability measures. In this paper, we first review both classical and modern lower bounds of reliability. Then, these measures are demonstrated by the analysis of several artificial and real datasets. The results coincided with the findings of Revelle & Zinbarg (2009) in that ωt is the most recommended lower bound.