Sales forecasting plays a crucial corporate role because it provides the basis for company-strategic decisions, including capacity preparation, inventory level, and capital expenditure budgets. Because of the uncertainty of sales forecasting errors, companies must increase costs to satisfy customer requirements and prepare a higher inventory level or capacity to avoid sales loss. Hence, sales forecasting accuracy has a considerable influence on company cost reduction.
In a foundry fab, the accuracy of sales forecasting is vital because the fab manufacturing cycle time is long, the lead time for capacity expansion requires considerable time and cost, and the capital investment is large. Therefore, sales forecasting is one of the most important jobs in a foundry fab.
Because of the importance of sales forecasting, it is crucial to establish a proper forecasting procedure to meet the accuracy requirement in a fab foundry. Hong-Sen  proposed that quantitative sales forecasting involves four stages: finding the main affecting factors, using the observational values of these factors within a certain period as the input of a certain regression model, determining the model parameters and structure by training, and providing forecasting results by extrapolation based on the trained model. Based on these four stages, the necessary cycles of sales forecasting include finding the affecting factors, choosing appropriate models, estimating the parameters of models with adequate methods, and evaluating the models. These four cycles are introduced in the following sections.
As the foundry fab industry is highly technological, Prior studies have focused on finding the affecting factors of sales forecasting. For example, new technology reduces manufacturing costs to increase sales. Chien et al.  proposed five factors for semiconductor demand: seasonal factors, market growth rate, price, repeat purchases, and technological substitution. This study forecast overall sales of an foundry fab so the effects of price, repeat purchases, and technological substitution will not be checked as it should be reviewed by technology. Therefore, this study only verifies the seasonal factors and market growth rate.
After determining the effects, it is crucial to identify the most suitable models to implement for sales forecasting in a foundry fab. The linear time series model and regression are commonly used. The linear time series model is one of the most popular tools. Except for it, after we reviewing all forecasting regression equations, the Bass diffusion model is widely used as the empirical adoption curve for technological innovations because it implements the exponential growth of initial purchases to a peak and exponentially decays, similar to technological innovation. Therefore, this study forecast the sales in a foundry fab with these two ways.
After determining the proper factors and regression model, it is crucial to improve the forecasting accuracy through parameters estimation. This study use MLE and NLS to estimate the parameters of linear time series model and the Bass diffusion, respectively. Then, this study verifies the result of the parameters estimation with the statistical methods. In addition, this study compares the forecast performance of these two methods. This study also predicts the sales trend in 2013.
2. Finding Affecting factors
We are interested the following two questions: Does the sales trend in a foundry fab exhibit upward trend? Does the sales trend in a foundry fab exhibit seasonal behavior? First of all, we should look the trend chart of sales before forecast. It shows...