After a work of Derman and Ross(1997) that considered simple main runs rules and derived ARL (Average Run Length) using Markov chain modeling, $ar{X}$ control chart based on diverse alternative main and supplementary runs rules that is the most popular control chart for monitoring the mean of a process are proposed. This paper reviews and discusses the-state-of-art researches for these runs rules and classifies according to several properties of runs rules. ARL derivation for a proposed runs rule is also illustrated.