Dynamic control charts for finite production runs

A dynamic programming model is developed for the optimization of statistical process control for finite production runs. The case of one-sided control charts for variables is examined first. A dynamic chart allows all three parameters, namely the sampling interval, sample size and control limit location, to change during production, as sample information becomes available and the state of the process is updated using Bayesian methods. The economic performance of the optimal dynamic chart is compared to that of the optimal static control chart through a number of numerical examples. It is concluded that substantial improvements may result from the adoption of dynamic charts. The benefits of direct observability of assignable causes are also estimated. Then, a generalized theoretical formulation is provided for two-sided dynamic control charts. The increased size of the state and decision spaces leads to a discussion of practical implementation issues. An example of computing transition probabilities between states of different stages is given. The major conclusion of this research is that significant cost savings may be realized through the application of dynamic control charts and even greater benefits may be reaped by investing in process understanding and improvements.