The innovation cumulative sum chart

This paper investigates the acceptable quality level under which quality characteristics have a normal probability distribution with an unknown location parameter. The traditional cumulative sum depends on the unknown parameter, and hence can not be used. Replacing the unknown parameter by its estimator yields the estimated cumulative sum, but the replacement clearly affects the behavior under the acceptable quality level. To overcome this problem, the innovation cumulative sum is proposed. The innovation cumulative sum performs at least as good as the estimated cumulative sum under a linear trend rejectable quality level, and clearly performs better for a rejectable quality level with the change point occurring in the first 70 percent of the sample. Finally, the definition of the innovation cumulative sum is extended for acceptable quality levels involving quality characteristics having a non-normal distribution.