Economic Design of Fraction Defective Control Charts

An expected cost model for the fraction defective control chart for the case where there are several out-of-control states is developed. A procedure is presented for determining the sample size, control limit or critical region, and interval between samples which minimizes the expected cost of control per unit of product. The expected cost of control consists of the cost of sampling, the cost of investigating and possibly correcting the process when an out-of-control condition is indicated, and the cost of producing defective product. Direct search techniques are used to optimize the expected cost function. Numerical examples and sensitivity analysis of the model are presented.