Designing an effective exponential cusum chart without the use of nomographs

The development of control charts for monitoring processes associated with very low rates of nonconformities is increasingly becoming more important as manufacturing processes become more capable. Since the rate of nonconformities can typically be modeled by a simple homogeneous Poisson process, the perspective of monitoring the interarrival times using the exponential distribution becomes an alternative. Gan (1994) developed a CUSUM-based approach for monitoring the exponential mean. In this paper, we propose an alternative CUSUM-based approach based on its ease of implementation. We also provide a study of the relative performance of the two approaches.