Different normality-based optimization strategy (NBOS) methods have been developed and used to perform quality improvement in the past few decays. Improving the quality of a production process using a NBOS method possibly incurs misleading results if the quality measurements follow a skewed distribution. An integrated model, with components of a tolerance cost model for the determinations of optimal tolerance limits and a quality investment model for the identification of optimal investment level, is applied to establish a new optimization strategy method for the skew normal distribution (SND), named SNDOS method. The SND generalizes the normal distribution to include skewed distributions as members, and hence the SNDOS method is applicable for quality improvement either the distribution of quality measurements follow a symmetric or skewed distribution. Two examples about car seat production process are used to illustrate the application of the SNDOS method. The sensitivity of the SNDOS method to the loss coefficient of the integrated model is evaluated for different inputs of the skewness parameter of the SND through a numerical study.