In this section we provide the basic structures of Tukey and CUSUM charts and then the proposed Tukey-CUSUM chart. Let Yi (i=1,2,3,...,n) be the independent and identically distributed random observations following a specific probability model that may be normal or non-mormal. Let mu0 and gamma0 be the process mean and dispersion respectively. Based on this information the design structures of the three aforementioned charts are given below.