Simultaneous acceptance control charts for products with multiple correlated characteristics

Acceptance control charts establish control limits based on specification limits for very capable processes where the mean is permitted to vary. This paper deals with designing such charts when a product has two or more correlated characteristics that must all simultaneously conform to specification limits for the product to be acceptable. The authors extend past work by solving the general correlated multivariate case, and by allowing a more general hypothesis test. They find the control limits and sample sizes for each characteristic that minimize sampling costs. The problem is a convex nonlinear optimization problem, and optimal solutions are found using multidimensional search.