Efficiently controlling the early stages of a manufacturing system is an important issue for enterprises. However, the number of samples collected at this point is usually limited due to time and cost issues, making it difficult to understand the real situation in the production process. One of the ways to solve this problem is to use a small data set forecasting tool, such as the various grey approaches. The grey model is a popular forecasting technique for use with small data sets, and while it has been successfully adopted in various fields, it can still be further improved. This paper thus uses a box plot to analyze data features and proposes a new formula for the background values in the grey model to improve forecasting accuracy. The new forecasting model is called SLIEGM(1,1). In the experimental study, one public dataset are used to confirm the effectiveness of the proposed model, and the experimental results show that it is an appropriate tool for small data set forecasting.