Double Objective Economic - Statistical Design under Pareto Shock models

The technique of control charts to monitor process behavior is one of the basic tools of statistical process control. Process changes can be divided into two main categories: common (random) cause, which is a fundamental feature of any process, and cause (definable) deviation, the occurrence of which is an unusual disorder that must be eliminated in order for the process to reverse. The main purpose of using management control charts is to separate these two different sources.Control charts are widely used in the analysis and control of production processes to produce satisfactory, sufficient, reliable and economical quality. Optimizing chart parameters is an important issue for quality engineers to improve processes. In this paper, the economic statistical design of the X ̅ control chart under the Pareto shock model based on the double objective design is presented. Actually by applying restrictions on the first type of error, the cost as the economic objective and the second type of error as the statistical objective is considered and then the optimal solutions are selected based on the Pareto front. Finally, through a practical example, the advantages of the proposed approach are shown by preparing a list of optimal solutions and graphical representations.