Statistical process control subject to a labour resource constraint

We develop a method for finding the economic sampling plan that minimizes expected total costs, subject to a constraint on labour time. We explicitly recognize the labour time required for sampling, investigation, extra processing effort per unit due to operating the process out of control, and the time to put the process back into control. These times, as well as the total production time, are frequently constrained by total available labour. With this constraint, we use a Lagrangian relaxation method to find the best sampling plan. Results of a numerical experiment show that the labour-constrained sampling plans and costs can differ substantially from the unconstrained solution. However, much of the cost penalty when labour is tightly constrained can be reduced with relatively small increases in total available labour time.