There has been considerable research on the economic design of Statistical Process Control models, for example nx charts. However, the effects of the nature of variability costs (cost due to process variation or, alternatively, the risk position of the firm) on the design parameters of such models have not been investigated. To examine the effects of variability cost, the authors develop a continuous shift model that plausibly assumes that a process mean stochastically undergoes numerous small, possibly undetectable shifts, some moderate size shifts, and a few larger shifts each having some cost. Using this continuous time model, they show in what manner the optimal design parameters of an nx chart are significantly affected by the nature of the variability cost function. Moreover, contrary to the results of past research, the authors show that under certain conditions, there can be significant differences in expected costs and design parameters between continuous and single shift models.
