Abstract A nonparametric two‐sample life test based on the order of early Failures–precedence test–is discussed. First, the basic idea of precedence‐type life‐testing procedures and some related works in the literature are reviewed. Then, some efficient alternatives for the precedence test are discussed which include the maximal precedence test, Wilcoxon‐type rank‐sum precedence tests, and the weighted precedence and maximal precedence tests with an extension to progressively censored data. Exact powers of these test procedures under the Lehmann alternative are discussed and evaluated numerically. Finally, applications of precedence‐type statistics to multisample selection problems are briefly mentioned.