AN ALGORITHM FOR THE DETERMINATION OF THE ECONOMIC DESIGN OF X-CHARTS BASED ON DUNCAN'S MODEL.

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]