The Economic Design of Sampling Control Strategies for a Class of Industrial Process

Abstract

Many authors have proposed models for the optimal design of control charts for the control of the defect rate for industrial processes. These models have limited the alternatives available subsequent to sampling to either rebuilding the process, or continuing to operate the process in its current state. Although the cost of rebuilding the process is treated as an adjustable parameter in these models, it can not be a negligible amount. If it were, the obvious optimal strategy would be to rebuild the process, possibly without samplings, after each batch or unit produced. This paper considers the determination of the optimal sample size and sample interval for the case where the process does not have to be rebuilt, but rather may be simply adjusted at a nominal cost after each sample. A model, which assumes a continuum of process fraction defectives, is developed and then used to explore the effect of fixed and variable sampling cost, specification limits and measurement errors on the optimal sampling policy and costs.