Economic and Economic-Statistical Designs of Phase II Profile Monitoring

In economic design of profiles, parameters of a profile are determined such that the total implementation cost is minimized. These parameters consist of the number of set points, n, the interval between two successive sampling, h, and the parameters of a control chart used for monitoring. In this paper, the Lorenzen-Vance cost function is extended to model the costs associated with implementing profiles. The in-control and the out-of-control average run lengths, ARL0 and ARL1, respectively are used as two statistical measures to evaluate the statistical performances of the proposed model. A genetic algorithm (GA) is developed for solving both the economic and the economic-statistical models, where response surface methodology is employed to tune the GA parameters. Results indicate satisfactory statistical performance without much increase in the cost of implementation.