On-line control procedures for integrated moving average process of order one

A commonly used model in process adjustment is the integrated moving average (IMA) process of order one. When the disturbances are normally distributed, this problem has been considered by Box and Jenkins (1963, 1976), Kramer (1989), Srivastava and Wu (1992), Box and Kramer (1992) and Srivastava (1996). Box and Lucefio (1994) extended the above model to any disturbance that is symmetrically distributed. However, their solution involves Fred holm integral equation which must be solved by numerical methods. In this paper, we follow the approach of Srivastava and Wu (1992, 1996) and provide the optimum control limit explicitly in terms of the first moment of the randomly stopped random sum of independent and identically distributed observations. These results are also used to study the robustness of the normal model. It is shown that the procedure is robust for small to moderate departure from normality.