Optimal process levels for the joint control of variables and attributes

This paper presents an economic model which incorporates the joint control of both variable and attribute quality characteristics of a product. Items are acceptable if they meet the specifications for both types of characteristics at the same time. Otherwise, the items are reprocessed or sold as scrap at a reduced price. A lot is acceptable if the number of rejected items does not exceed a given limit. The objective is to simultaneously select the appropriate target values for the characteristics, so as to maximize the expected income per lot. Optimality conditons are derived for various probability distributions of the number of defects in a lot and computational experience is reported.