Economically Designed Bayesian np Control Charts Using Dual Sample Sizes for Long-Run Processes

The implementation of a control chart requires the determination of three design parameters: the sample size, the sampling interval, and the control limits under which the production process will be stopped for potential repair. For a static control chart, the design parameters are maintained at the same level from an inspection epoch to another. Several research papers showed that adopting dynamic control charts in which one or more of the design parameters are allowed to vary from an inspection epoch to another leads to substantial cost savings compared to the classical ones. In this paper, we develop the expected long-run costs of two Bayesian np schemes, namely, the basic Bayesian and the Bayes-n charts for processes operating over an infinite horizon length. Optimal solutions leading to least-cost plans are searched for different sets of process and cost parameters. Experimental results show that moving from classical np control charts to Bayesian ones results in significant economic savings.