Quality Quandaries: Forecasting with Seasonal Time Series Models

As the scope of quality engineering is widening from primarily dealing with production floor issues to focusing on any type of operational problems company wide, quality engineers increasingly find themselves involved with a variety of more strategic quality problems. One such problem is improving the quality of forecasts as an aid to better planning, scheduling and ultimately better customer service. For example, the relationship between sales forecasting and operational planning for a typical manufacturing company is illustrated in Figure 1. The diagram shows how production volume, product mix, inventory levels, staffing, raw materials purchase, etc., all are related to sales. Similarly, if the operation is a service, good quality forecasts are critical for maintaining a high service level. The relationship between sales forecasts and airline operation decisions is schematically illustrated in Figure 2. For example, suppose we are helping an airline reducing cost and improving the quality of its services. In that case it would be important to be able to have available good quality forecasts for the number of airline passengers for a specific time period. In previous Quality Quandaries columns (Bisgaard and Kulahci, 2005a, 2005b, 2006a, 2006b, 2007a, 2007b, 2007c, 2008) we demonstrated with detailed examples how autoregressive integrated moving average (ARIMA) models can be used to model stationary and non-stationary time series. In this column we continue this discussion and show how seasonal data can be modeled and used for forecasting. We use the international airline data originally analyzed by Brown (1962) and modeled with a seasonal auto-regressive integrated moving average time series model by Box and Jenkins (1970) to demonstrate how seasonal ARIMA models can be used to model cyclic data and how the model can be used for short term forecasting. The data is available as series G in Box et al. (1994) and is reproduced in Table 1.