A new two-sided cumulative sum quality control scheme is proposed. The new scheme was developed specifically to be generalized to a multivariate cumulative sum quality control scheme. The multivariate version will be examined in a subsequent paper; this article evaluates the univariate version. A comparison of the conventional two-sided cumulative sum scheme and the proposed scheme indicates that the new scheme has slightly better properties (ratio of on-aim to off-aim average run lengths) than the conventional scheme. Steady state average run lengths are discussed. The new scheme and the conventional two-sided cumulative sum scheme have equivalent steady state average run lengths. Methods for implementing the fast initial response feature for the new cumulative sum scheme are given. A comparison of average run lengths for the conventional and proposed schemes with fast initial response features is also favorable to the new scheme. A Markov chain approximation is used to calculate the average run lengths of the new scheme.