Abstract: According to different cases of normal-distribution process parameters (\mu,\sigma^2), several problems are studied in this paper, for monitoring the process with parameters known or unknown, with single-parameter-deviation or with double-parameter-deviation. A series of CUSUM Charts are proposed in standardized or simpler forms mainly based on Q-statistics proposed by Quesenberry. In the last part of the paper, the concept of deviation-interested-only (DIO) is put forward and the relevant statistics are given where there is no need to know which has deviated, process mean or process variance. The simulation results of Conditional Expected Delay (CED) are shown in each case, and the comparisons in the end of the paper show which new CUSUM charts act well.